24 Density, Yield & Gravimetric Air (ASTM C138) Practice Questions & Answers

Every Density, Yield & Gravimetric Air (ASTM C138) practice question from the ACI Concrete Field Testing Technician Grade I Practice Test, with the correct answer and a short explanation.

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1. Under ASTM C138/C138M, how is the gravimetric air content of fresh concrete determined?
- A.By rolling the sample with water and alcohol and reading the air volume displaced in the neck
- B.By pressurizing the sealed bowl and reading the drop in pressure as air on a calibrated gauge
- C.By comparing the mix's theoretical air-free density with the density measured in the filled measure✓ Answer
- D.By dividing the net mass of concrete in the measure by the total mass of water in the batch
Gravimetric air content is calculated, not measured directly: the air-free theoretical density T from the batch masses and absolute volumes is compared with the measured density D, and the shortfall (T - D)/T is the air. Pressurizing a bowl is the C231/C231M pressure method and rolling with alcohol is the C173/C173M volumetric method.
Ref QB-RR9RXDSource: ASTM C138/C138M, Standard Test Method for Density (Unit Weight), Yield, and Air Content (Gravimetric) of Concrete — scope; gravimetric air content from theoretical and measured densityReport a problem with this question
2. Why must the volume of a density (unit weight) measure be calibrated rather than simply taken from its nominal size?
- A.Its calibration sets the balance tare, so the empty-measure mass no longer has to be recorded in the field
- B.Its nominal figure already includes an allowance for concrete left on the rim, so it always reads too high
- C.Its calibration only matters for lightweight concrete, since normal-weight results are rounded off anyway
- D.Its true volume can differ from the nominal figure, and any volume error passes straight into the density✓ Answer
Density is net concrete mass divided by the measure's volume, so the volume is a direct divisor: manufacturing tolerance, dents and wear make the real volume differ from the nominal size, and that difference shows up one-for-one in density, yield and gravimetric air. The volume is therefore determined by the water-filling calibration and rechecked periodically; it does not replace weighing the empty measure.
Ref QB-894KCDSource: ASTM C138/C138M, Standard Test Method for Density (Unit Weight), Yield, and Air Content (Gravimetric) of Concrete — calibrated volume of the measure (water method of ASTM C29/C29M)Report a problem with this question
3. Why does ASTM C138/C138M require a larger minimum measure capacity as the nominal maximum size of the coarse aggregate increases?
- A.A larger measure cancels balance error, which is the real reason capacity follows aggregate size
- B.A larger measure keeps the sample representative, so a few big stones cannot skew the density✓ Answer
- C.A larger measure lets the technician skip rodding, since big stones consolidate under their weight
- D.A larger measure is needed to hold enough mortar for the pressure air test run on that sample
With large coarse aggregate, each particle is a big fraction of a small container, and the wall effect and the chance placement of a few stones would make the measured mass unrepresentative of the mix. A bigger measure averages these out, which is why the minimum capacity rises with nominal maximum size. Consolidation is still required at every size.
Ref QB-QRWDSCSource: ASTM C138/C138M, Standard Test Method for Density (Unit Weight), Yield, and Air Content (Gravimetric) of Concrete — capacity of measure versus nominal maximum size of coarse aggregateReport a problem with this question
4. A paving mix is so stiff that its slump is well under 1 in. (25 mm). How should the technician consolidate the concrete in the density (unit weight) measure?
- A.Use internal vibration, since rodding cannot fully consolidate concrete that stiff✓ Answer
- B.Use rodding with extra strokes, since a stiff mix only needs more compactive effort
- C.Use rodding alone, since vibration drives entrained air out of any low-slump mix
- D.Use mallet taps alone, since a stiff mix would trap the rod and leave large voids
C138/C138M selects the consolidation method by slump: high-slump concrete is rodded, intermediate slump may be rodded or vibrated, and very low-slump concrete must be internally vibrated because rodding cannot remove the voids in so stiff a mix. Adding rod strokes does not solve that, and mallet tapping only supplements consolidation.
Ref QB-79R87CSource: ASTM C138/C138M, Standard Test Method for Density (Unit Weight), Yield, and Air Content (Gravimetric) of Concrete — selection of consolidation method by slumpReport a problem with this question
5. While vibrating an air-entrained mix in the measure, a technician keeps the vibrator running long after the surface has become smooth. What effect will this most likely have on the C138/C138M results?
- A.Entrained air is driven out, so the density reads high and the gravimetric air reads low✓ Answer
- B.Mortar rises and is struck off, so the density reads low and the yield reads too high
- C.Coarse stones settle to the bottom, which has no effect as long as the measure is full
- D.Bleed water rises and evaporates, so the density reads high and the yield reads high
Over-vibration expels entrained air, so the measure holds more solid material per unit volume: the measured density rises, and because yield is batch mass divided by density and gravimetric air is (T - D)/T, the yield and the air content both come out too low. Vibration should stop once the surface is relatively smooth.
Ref QB-PRJ3MBSource: ASTM C138/C138M, Standard Test Method for Density (Unit Weight), Yield, and Air Content (Gravimetric) of Concrete — consolidation by internal vibration; avoiding over-vibrationReport a problem with this question
6. A technician rods each layer in the density measure but skips tapping the sides, so rod holes and large bubbles remain. How does this affect the calculated results?
- A.Density reads high, so yield is understated and the gravimetric air content reads low
- B.Density reads low, so yield is overstated and the gravimetric air content reads high✓ Answer
- C.Density is unaffected, because voids left in the measure are not part of its volume
- D.Only the gravimetric air reads high; yield is unaffected, since it uses batch masses
Unclosed rod holes and trapped bubbles leave the calibrated volume only partly filled with concrete, so the net mass divided by that volume gives a density that is too low. Yield is total batch mass divided by density, so it comes out too high, and gravimetric air, which compares measured density with the air-free theoretical density, comes out too high as well.
Ref QB-ENYU6GSource: ASTM C138/C138M, Standard Test Method for Density (Unit Weight), Yield, and Air Content (Gravimetric) of Concrete — procedure (tapping each layer) and calculation of density, yield and air contentReport a problem with this question
7. After the final layer has been consolidated, how should the technician finish the top of the measure before weighing it?
- A.Scrape the surplus away with the edge of the scoop, then add mortar to fill any low spots left
- B.Screed it with the tamping rod rolled across the rim until most of the surplus has been removed
- C.Strike it off with a flat plate in a sawing motion until the concrete is just level with the rim✓ Answer
- D.Trowel the surface smooth and leave a slight crown so the measure is sure to be completely full
The density calculation assumes the measure holds exactly its calibrated volume, so the top must be struck off with a flat strike-off plate, using pressure and a sawing motion, until it is just level full and smooth. A rod screed or a crowned surface leaves excess or missing concrete, and adding mortar changes the sample's proportions.
Ref QB-NR7REASource: ASTM C138/C138M, Standard Test Method for Density (Unit Weight), Yield, and Air Content (Gravimetric) of Concrete — strike-off with the strike-off plateReport a problem with this question
8. Concrete has splashed onto the outside wall and rim of the filled measure. What should the technician do before determining the filled mass, and why?
- A.Clean it all off, since concrete outside the calibrated volume would inflate the density✓ Answer
- B.Weigh it as is and subtract an estimate, since cleaning could disturb the struck surface
- C.Leave it in place, since the same splash was there when the empty measure was weighed
- D.Ignore it entirely, since a little extra mass is within the accuracy of the field balance
Only concrete inside the calibrated volume belongs in the net mass. Any concrete on the exterior or rim adds mass with no matching volume, so it raises the computed density and lowers the yield and gravimetric air; all excess must be cleaned from the outside before the filled measure is weighed. The empty measure was weighed clean, so the splash is not cancelled out.
Ref QB-D9V88KSource: ASTM C138/C138M, Standard Test Method for Density (Unit Weight), Yield, and Air Content (Gravimetric) of Concrete — cleaning the exterior and determining the mass of the filled measureReport a problem with this question
9. A technician uses a calibrated air-meter bowl that meets C231/C231M as the density (unit weight) measure. Once the struck-off bowl has been weighed, what may be done with that concrete?
- A.It may be used for the volumetric air test, since that meter accepts any calibrated air bowl
- B.It may be remixed into the sample and used to mold cylinder specimens for strength acceptance
- C.It may go straight on to the pressure air test, since it is already consolidated in the bowl✓ Answer
- D.It may be used for a slump test, since rodding in the bowl has already settled the concrete
When the measure is a C231/C231M air-meter bowl whose volume has been calibrated, the consolidated, struck-off and weighed concrete is exactly the condition the pressure test needs, so the cover can be clamped on and the air test run on the same sample. Concrete already consolidated and tested should not be reused for slump or cylinders, and a volumetric meter uses its own matched bowl and top section.
Ref QB-VRP3NJSource: ASTM C138/C138M, Standard Test Method for Density (Unit Weight), Yield, and Air Content (Gravimetric) of Concrete — use of an air-meter bowl as the measureReport a problem with this question
10. A load of concrete is tested and its relative yield works out to 0.96. What does this result indicate?
- A.The batch made more concrete than ordered, so its cement per cubic yard is lower than designed
- B.The batch made the volume ordered, and the 4% gap is simply the air measured gravimetrically
- C.The batch made less concrete than ordered, so its cement per cubic yard is lower than designed
- D.The batch made less concrete than ordered, so its cement per cubic yard is higher than designed✓ Answer
Relative yield is actual yield divided by designed yield, so a value below 1.00 means under-yield: the customer received less volume than was paid for. The same mass of cement is spread over a smaller volume, so the actual cement content per cubic yard (cement mass divided by actual yield) is higher than designed. Relative yield is not an air content.
Ref QB-74JN8JSource: ASTM C138/C138M, Standard Test Method for Density (Unit Weight), Yield, and Air Content (Gravimetric) of Concrete — relative yield and actual cement contentReport a problem with this question
11. Why is gravimetric air content generally regarded as less reliable than air content measured by the pressure or volumetric method?
- A.It ignores entrained air entirely and detects only the large entrapped voids left after rodding
- B.It is run on a wet-sieved sample, so air carried in the coarse aggregate fraction is not counted
- C.It relies on a field balance that cannot read finely enough to detect any change in air content
- D.It depends on accurate batch masses and on the specific gravity and moisture of each ingredient✓ Answer
Gravimetric air is computed from the theoretical air-free density, which depends on the reported batch masses, the specific gravities of cement, SCMs and aggregates, and the aggregate moisture and absorption; errors in any of these shift T and therefore the air result. The pressure and volumetric methods measure air in the sample directly, and C138/C138M is run on the full mixture rather than a sieved sample.
Ref QB-QKQTTJSource: ASTM C138/C138M, Standard Test Method for Density (Unit Weight), Yield, and Air Content (Gravimetric) of Concrete — significance and use; limitations of gravimetric air contentReport a problem with this question
12. A density (unit weight) test gives these data: filled measure 41.20 lb, empty measure 6.40 lb, calibrated volume of the measure 0.248 ft³ (nominal size 0.25 ft³). What is the density of the concrete?
- A.140.3 lb/ft³✓ Answer
- B.139.2 lb/ft³
- C.166.1 lb/ft³
- D.159.7 lb/ft³
Density is net concrete mass over calibrated volume: (41.20 - 6.40) / 0.248 = 34.80 / 0.248 = 140.3 lb/ft³. Dividing by the nominal 0.25 ft³ gives 139.2; forgetting to subtract the empty measure gives 41.20 / 0.248 = 166.1; dividing the filled mass first and then subtracting the empty mass gives 159.7.
Ref QB-647B3HSource: ASTM C138/C138M, Standard Test Method for Density (Unit Weight), Yield, and Air Content (Gravimetric) of Concrete — calculation of density: D = (Mc - Mm) / VmReport a problem with this question
13. To calibrate a measure, a technician records: empty measure plus glass plate 8.40 lb; measure filled with water and covered with the plate 23.92 lb; density of water at the test temperature 62.32 lb/ft³. What is the calibrated volume of the measure?
- A.0.3838 ft³
- B.0.2490 ft³✓ Answer
- C.0.2500 ft³
- D.0.2487 ft³
The calibrated volume is the mass of water held divided by the density of water at that temperature: (23.92 - 8.40) / 62.32 = 15.52 / 62.32 = 0.2490 ft³. Using a rounded 62.4 lb/ft³ instead of the temperature-specific value gives 0.2487; dividing the gross mass without subtracting the measure and plate gives 0.3838; simply assuming the nominal size gives 0.2500.
Ref QB-PKCGNHSource: ASTM C138/C138M, Standard Test Method for Density (Unit Weight), Yield, and Air Content (Gravimetric) of Concrete — calibrated volume of the measure (water method of ASTM C29/C29M)Report a problem with this question
14. A 9.0 yd³ batch contains cement 5,040 lb, fine aggregate 12,150 lb, coarse aggregate 15,750 lb (both as batched, including free moisture) and water 2,160 lb. The measured density is 144.0 lb/ft³, and the mix design's air-free theoretical density is 150.0 lb/ft³. What is the yield of the batch?
- A.234.0 ft³
- B.243.0 ft³
- C.243.8 ft³✓ Answer
- D.228.8 ft³
Yield is total batch mass divided by measured density: M = 5,040 + 12,150 + 15,750 + 2,160 = 35,100 lb, and 35,100 / 144.0 = 243.8 ft³. Reporting the ordered 9.0 x 27 = 243.0 ft³ skips the measurement; leaving out the water gives 32,940 / 144.0 = 228.8; dividing by the theoretical density instead of the measured density gives 234.0.
Ref QB-949BKMSource: ASTM C138/C138M, Standard Test Method for Density (Unit Weight), Yield, and Air Content (Gravimetric) of Concrete — calculation of yield: Y = M / DReport a problem with this question
15. A batch ordered as 10.0 yd³ has a total mass of all batched materials of 40,500 lb. The measured density is 146.0 lb/ft³ and the mix's theoretical air-free density is 152.0 lb/ft³. What is the yield in cubic yards?
- A.92.47 yd³
- B.9.87 yd³
- C.277.40 yd³
- D.10.27 yd³✓ Answer
Yield in cubic yards is M / (27 x D) because there are 27 ft³ in a cubic yard: 40,500 / (27 x 146.0) = 40,500 / 3,942 = 10.27 yd³. Using the theoretical density gives 9.87; never converting from cubic feet leaves 277.40; dividing by 3, as if converting a length, gives 92.47.
Ref QB-SKEG6NSource: ASTM C138/C138M, Standard Test Method for Density (Unit Weight), Yield, and Air Content (Gravimetric) of Concrete — calculation of yield in cubic yards: Y = M / (27 x D)Report a problem with this question
16. A batch ordered as 10.0 yd³ has a total batch mass of 37,800 lb. In the density test the filled measure weighed 40.30 lb, the empty measure 4.05 lb, and the calibrated volume was 0.250 ft³. What is the relative yield?
- A.1.04
- B.0.97✓ Answer
- C.1.15
- D.0.87
First D = (40.30 - 4.05) / 0.250 = 145.0 lb/ft³, then Y = 37,800 / (27 x 145.0) = 9.66 yd³, and relative yield is actual over designed: 9.66 / 10.0 = 0.97. Inverting the ratio (10.0 / 9.66) gives 1.04; forgetting to subtract the empty measure makes D = 161.2 and the ratio 0.87; making both mistakes gives 1.15.
Ref QB-84WYDKSource: ASTM C138/C138M, Standard Test Method for Density (Unit Weight), Yield, and Air Content (Gravimetric) of Concrete — calculation of relative yield: Ry = Y / YdReport a problem with this question
17. A batch ordered as 10.0 yd³ was designed for 564 lb of cement per cubic yard, so it contains 5,640 lb of cement. Tests show its actual yield is 9.40 yd³, a relative yield of 0.94. What is the actual cement content?
- A.22.2 lb/yd³
- B.600.0 lb/yd³✓ Answer
- C.564.0 lb/yd³
- D.530.2 lb/yd³
Actual cement content is the cement mass divided by the actual yield: 5,640 / 9.40 = 600.0 lb/yd³, higher than designed because the batch under-yielded. Dividing by the ordered 10.0 yd³ returns the design value 564.0; dividing by the yield in cubic feet (9.40 x 27) gives 22.2; multiplying the design content by the relative yield instead of dividing gives 530.2.
Ref QB-RK36ZKSource: ASTM C138/C138M, Standard Test Method for Density (Unit Weight), Yield, and Air Content (Gravimetric) of Concrete — calculation of actual cement content: N = Nt / YReport a problem with this question
18. For one cubic yard of a mix, the batch masses and absolute volumes are: cement 564 lb (2.87 ft³), water 282 lb (4.52 ft³), coarse aggregate 1,850 lb (11.06 ft³) and fine aggregate 1,250 lb (7.65 ft³). What is the theoretical air-free density?
- A.151.2 lb/ft³✓ Answer
- B.169.8 lb/ft³
- C.146.1 lb/ft³
- D.140.4 lb/ft³
Theoretical density is total mass divided by the sum of absolute volumes, which excludes air: M = 3,946 lb and V = 2.87 + 4.52 + 11.06 + 7.65 = 26.10 ft³, so T = 3,946 / 26.10 = 151.2 lb/ft³. Dividing by the full 27 ft³, which includes air, gives 146.1; leaving the water out of the mass only gives 140.4; leaving water out of both mass and volume gives 169.8.
Ref QB-B4YYWPSource: ASTM C138/C138M, Standard Test Method for Density (Unit Weight), Yield, and Air Content (Gravimetric) of Concrete — calculation of theoretical density: T = M / VReport a problem with this question
19. A mix has a theoretical air-free density of 150.8 lb/ft³, and the measured density of the fresh concrete is 142.6 lb/ft³. What is the gravimetric air content?
- A.8.2%
- B.5.8%
- C.5.4%✓ Answer
- D.94.6%
Gravimetric air is the density shortfall as a fraction of the theoretical density: A = (150.8 - 142.6) / 150.8 x 100 = 5.4%. Dividing by the measured density instead of T gives 5.8%; reporting the raw density difference as a percentage gives 8.2%; computing D / T gives the solids fraction, 94.6%, not the air.
Ref QB-UK56HQSource: ASTM C138/C138M, Standard Test Method for Density (Unit Weight), Yield, and Air Content (Gravimetric) of Concrete — calculation of air content: A = [(T - D) / T] x 100Report a problem with this question
20. A batch has a measured yield of 271.5 ft³. The sum of the absolute volumes of all its ingredients is 256.0 ft³, and it was designed to yield 270.0 ft³. What is its gravimetric air content?
- A.6.1%
- B.5.7%✓ Answer
- C.5.2%
- D.15.5%
In yield terms, air is the part of the actual volume not occupied by solids and water: A = (Y - V) / Y x 100 = (271.5 - 256.0) / 271.5 x 100 = 5.7%. Dividing by V instead of Y gives 6.1%; using the designed 270.0 ft³ in place of the measured yield gives 5.2%; reporting the 15.5 ft³ difference as a percentage gives 15.5%.
Ref QB-M28UF2Source: ASTM C138/C138M, Standard Test Method for Density (Unit Weight), Yield, and Air Content (Gravimetric) of Concrete — calculation of air content from yield: A = [(Y - V) / Y] x 100Report a problem with this question
21. A density test gives: filled measure 40.10 lb, empty measure 4.35 lb, calibrated volume 0.2475 ft³ (nominal 0.25 ft³). The mix's theoretical air-free density is 151.0 lb/ft³. What is the gravimetric air content?
- A.4.5%
- B.4.3%✓ Answer
- C.6.6%
- D.5.3%
First D = (40.10 - 4.35) / 0.2475 = 35.75 / 0.2475 = 144.4 lb/ft³, then A = (151.0 - 144.4) / 151.0 x 100 = 4.3%. Using the nominal 0.25 ft³ makes D = 143.0 and A = 5.3%; dividing the difference by D instead of T gives 4.5%; reporting the 6.6 lb/ft³ difference itself as a percentage gives 6.6%.
Ref QB-4J2PVZSource: ASTM C138/C138M, Standard Test Method for Density (Unit Weight), Yield, and Air Content (Gravimetric) of Concrete — calculation of density and gravimetric air contentReport a problem with this question
22. A 10.0 yd³ (270.0 ft³) batch has a total mass of 39,150 lb, and the sum of the absolute volumes of its ingredients is 261.0 ft³. The measured density is 142.5 lb/ft³. What is the gravimetric air content?
- A.1.7%
- B.5.3%
- C.5.0%✓ Answer
- D.7.5%
The theoretical density uses the air-free absolute volume: T = 39,150 / 261.0 = 150.0 lb/ft³, so A = (150.0 - 142.5) / 150.0 x 100 = 5.0%. Dividing by D instead of T gives 5.3%; computing T from the designed 270.0 ft³, which already contains air, gives T = 145.0 and A = 1.7%; reporting the 7.5 lb/ft³ difference as a percentage gives 7.5%.
Ref QB-K2VGAZSource: ASTM C138/C138M, Standard Test Method for Density (Unit Weight), Yield, and Air Content (Gravimetric) of Concrete — calculation of theoretical density and air contentReport a problem with this question
23. A batch has a total mass of 38,610 lb. In the density test the filled measure weighed 39.90 lb, the empty measure 4.25 lb, and the calibrated volume was 0.2485 ft³ (nominal 0.25 ft³). What is the yield in cubic yards?
- A.8.91 yd³
- B.269.13 yd³
- C.10.03 yd³
- D.9.97 yd³✓ Answer
D = (39.90 - 4.25) / 0.2485 = 35.65 / 0.2485 = 143.46 lb/ft³, so Y = 38,610 / (27 x 143.46) = 9.97 yd³. Using the nominal 0.25 ft³ gives D = 142.6 and 10.03; forgetting to subtract the empty measure gives D = 160.56 and 8.91; skipping the division by 27 leaves the cubic-foot value 269.13.
Ref QB-3JPBQYSource: ASTM C138/C138M, Standard Test Method for Density (Unit Weight), Yield, and Air Content (Gravimetric) of Concrete — calculation of density and yield in cubic yardsReport a problem with this question
24. A batch contains 600 lb of cement with a specific gravity of 3.15. Taking the density of water as 62.4 lb/ft³, what is the absolute volume of the cement?
- A.9.62 ft³
- B.190.48 ft³
- C.30.29 ft³
- D.3.05 ft³✓ Answer
Absolute volume is mass divided by the product of specific gravity and the density of water: 600 / (3.15 x 62.4) = 600 / 196.56 = 3.05 ft³. Ignoring the specific gravity gives 600 / 62.4 = 9.62; multiplying by the specific gravity instead of dividing gives 30.29; dividing by the specific gravity alone gives 190.48.
Ref QB-J2H65YSource: ASTM C138/C138M, Standard Test Method for Density (Unit Weight), Yield, and Air Content (Gravimetric) of Concrete — absolute volume of ingredients for theoretical densityReport a problem with this question

1. Under ASTM C138/C138M, how is the gravimetric air content of fresh concrete determined?

2. Why must the volume of a density (unit weight) measure be calibrated rather than simply taken from its nominal size?

3. Why does ASTM C138/C138M require a larger minimum measure capacity as the nominal maximum size of the coarse aggregate increases?

4. A paving mix is so stiff that its slump is well under 1 in. (25 mm). How should the technician consolidate the concrete in the density (unit weight) measure?

5. While vibrating an air-entrained mix in the measure, a technician keeps the vibrator running long after the surface has become smooth. What effect will this most likely have on the C138/C138M results?

6. A technician rods each layer in the density measure but skips tapping the sides, so rod holes and large bubbles remain. How does this affect the calculated results?

7. After the final layer has been consolidated, how should the technician finish the top of the measure before weighing it?

8. Concrete has splashed onto the outside wall and rim of the filled measure. What should the technician do before determining the filled mass, and why?

9. A technician uses a calibrated air-meter bowl that meets C231/C231M as the density (unit weight) measure. Once the struck-off bowl has been weighed, what may be done with that concrete?

10. A load of concrete is tested and its relative yield works out to 0.96. What does this result indicate?

11. Why is gravimetric air content generally regarded as less reliable than air content measured by the pressure or volumetric method?

12. A density (unit weight) test gives these data: filled measure 41.20 lb, empty measure 6.40 lb, calibrated volume of the measure 0.248 ft³ (nominal size 0.25 ft³). What is the density of the concrete?

13. To calibrate a measure, a technician records: empty measure plus glass plate 8.40 lb; measure filled with water and covered with the plate 23.92 lb; density of water at the test temperature 62.32 lb/ft³. What is the calibrated volume of the measure?

15. A batch ordered as 10.0 yd³ has a total mass of all batched materials of 40,500 lb. The measured density is 146.0 lb/ft³ and the mix's theoretical air-free density is 152.0 lb/ft³. What is the yield in cubic yards?

16. A batch ordered as 10.0 yd³ has a total batch mass of 37,800 lb. In the density test the filled measure weighed 40.30 lb, the empty measure 4.05 lb, and the calibrated volume was 0.250 ft³. What is the relative yield?

17. A batch ordered as 10.0 yd³ was designed for 564 lb of cement per cubic yard, so it contains 5,640 lb of cement. Tests show its actual yield is 9.40 yd³, a relative yield of 0.94. What is the actual cement content?

18. For one cubic yard of a mix, the batch masses and absolute volumes are: cement 564 lb (2.87 ft³), water 282 lb (4.52 ft³), coarse aggregate 1,850 lb (11.06 ft³) and fine aggregate 1,250 lb (7.65 ft³). What is the theoretical air-free density?

19. A mix has a theoretical air-free density of 150.8 lb/ft³, and the measured density of the fresh concrete is 142.6 lb/ft³. What is the gravimetric air content?

20. A batch has a measured yield of 271.5 ft³. The sum of the absolute volumes of all its ingredients is 256.0 ft³, and it was designed to yield 270.0 ft³. What is its gravimetric air content?

21. A density test gives: filled measure 40.10 lb, empty measure 4.35 lb, calibrated volume 0.2475 ft³ (nominal 0.25 ft³). The mix's theoretical air-free density is 151.0 lb/ft³. What is the gravimetric air content?

22. A 10.0 yd³ (270.0 ft³) batch has a total mass of 39,150 lb, and the sum of the absolute volumes of its ingredients is 261.0 ft³. The measured density is 142.5 lb/ft³. What is the gravimetric air content?

23. A batch has a total mass of 38,610 lb. In the density test the filled measure weighed 39.90 lb, the empty measure 4.25 lb, and the calibrated volume was 0.2485 ft³ (nominal 0.25 ft³). What is the yield in cubic yards?

24. A batch contains 600 lb of cement with a specific gravity of 3.15. Taking the density of water as 62.4 lb/ft³, what is the absolute volume of the cement?

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