Chapter 3 – Volume and Capacity Test Review Questions
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____
1. Which of the following statements about volume and/or capacity is not true?
a.
b.
c.
d.
____
Volume is the amount of three-dimensional space occupied by an object.
Capacity can be measured in litres.
Solid objects always have volume and capacity.
Volume is measured in cubed units.
2. What is the volume of the box shown?
35 cm
39 cm
27 cm
a. 33170 cm3
b. 36855 cm3
____
3. What is the volume of a cube with side lengths of 20 inches?
a. 7200 in3
b. 9600 in3
____
c. 8000 in3
d. 6400 in3
4. What is the volume of an aluminum can with a height of 8 inches and a radius of 1.5 inches?
a. 57 in3
b. 51 in3
____
c. 29484 cm3
d. 44226 cm3
c. 46 in3
d. 68 in3
5. A farmer’s cylindrical silo has a radius of 1.5 m and is filled with grain to a height of 7 m.
He is using the grain to fill bags that are 30 cm by 50 cm by 70 cm. How many bags will he be able to fill?
a. 539
b. 472
c. 349
d. 502
____
6. How many 500 cm3 bags of sugar will fit in a packing crate measuring 1.2 m by 1.1 m by 0.5 m?
a. 1350
b. 1387
____
c. 1320
d. 1197
7. What is the volume of this cylinder?
26 cm
26 cm
a. 55 284 cm3
b. 60 739 cm3
____
8. What are the dimensions of a cube with a volume of 1000 mm3?
a. 10 mm by 10 mm by 10 mm
b. 9 mm by 11 mm by 12 mm
____
c. 55 217 cm3
d. 16 565 cm3
c. 12 mm by 11 mm by 10 mm
d. 11 mm by 11 mm by 11 mm
9. Which of the following explains how to find the volume of a cylinder?
a.
b.
c.
d.
Volume of the base times height.
Area of the bases plus the area of the lateral face.
Area of the base times the height.
None of the above.
____ 10. A rectangular prism has dimensions l, w, and h. If the width is changed to 2w, how does the volume change?
a. The volume is doubled.
b. The volume is squared.
c. The volume is the same.
d. The volume is half as large.
____ 11. A rectangular prism has dimensions l, w, and h. If the width is changed to 2w and the length is changed to 2l,
how does the volume change?
a. The volume is 3 times larger.
b. The volume is doubled.
c. The volume is the same.
d. The volume is 4 times larger.
____ 12. A rectangular prism has dimensions l, w, and h. If the width is changed to 2w and the length is changed to 0.5l,
how does the volume change?
a. The volume is the same.
b. The volume is doubled.
c. The volume is 3 times larger.
d. The volume is 4 times larger.
____ 13. What is the volume of a sphere with a radius of 1.4 feet?
a. 9.2 ft3
b. 13.8 ft3
c. 11.5 ft3
d. 12.7 ft3
____ 14. What is the volume of a cone with a height of 37 feet and a diameter of 27 feet?
a. 5649.2 ft3
b. 8473.8 ft3
c. 7767.7 ft3
d. 7061.5 ft3
38 cm
____ 15. What is the volume of this pyramid?
30 cm
65 cm
a. 29640 cm3
b. 24700 cm3
c. 18525 cm3
d. 22230 cm3
____ 16. What amount of ice cream in litres can fit into a waffle cone with a diameter of 6 cm and a height of 15 cm?
(Imagine the ice cream fills the cone right to the top, and does not go above the edge of the cone.)
a. 0.15 L
b. 0.14 L
c. 0.17 L
d. 0.11 L
____ 17. By how much is the volume of a square-based pyramid increased when all the dimensions are doubled?
a. 400%
b. 800%
c. 200%
d. 100%
____ 18. What is the volume of the following cone?
4 cm
1.45 cm
a. 9.7 cm3
b. 7 cm3
c. 10.6 cm3
d. 8.8 cm3
____ 19. A parade includes a large spherical balloon. What is the capacity, in US gallons, of the balloon if it has a radius
of 25 feet? (There are 7.48 US gallons in a cubic foot.)
a. 538 522 US gal
b. 391 652 US gal
c. 587 478 US gal
d. 489 565 US gal
____ 20. What is the capacity, in litres, of sawdust in a cone-shaped pile 3 m high and 7.5 m wide across the base?
a. 44 000 L
b. 52 800 L
c. 35 200 L
d. 48 400 L
____ 21. What happens to the volume of a rectangular prism if one of its side lengths is tripled?
a. The volume multiplies by 3.
b.
The volume increases by .
c.
The volume decreases by
.
d. None of the above.
____ 22. What is the capacity, in litres, of a square-based pyramid with a height of 3.5 cm and side lengths of 8 cm?
a. 0.056 L
b. 0.075 L
c. 0.09 L
d. 0.068 L
Short Answer
1. The label on a thermos says it can hold 500 cm3 of liquid. But, if you measure the outside dimensions of the
thermos and use them to calculate the volume, its volume would be 550 cm3.
Give a possible explanation for the difference between the volume shows on the label and the volume
calculated.
2. Find the volume of a rectangular prism with the dimensions 5 cm by 12 cm by 4 cm.
3. What is the volume of the cylinder shown?
9.5 ft
18 ft
4. What is the capacity in litres of a cylinder that is 127 cm high with a radius of 4 cm?
5. Calculate the volume of a sphere with a radius of 233 ft.
6. Calculate the volume of a pyramid with a height of 80 m and a base with a length of 32 m and a width of 27 m.
7. Calculate the volume of a cone with a height of 1.1 m and a radius of 0.2 m.
8. What percentage of a sphere with a diameter of 60 cm would be filled by 20 L of water?
9. What is the volume of the figure below?
r = 11.5 cm
h = 19 cm
Problem
1. Jasmine is eating a mug of chicken noodle soup. Her mug is cylindrical, with a height of 8.5 cm and a radius of
2.75 cm.
a) What is the volume of the interior of the mug? (Ignore the thickness of the walls of the mug.)
b) What is the maximum amount of soup Jasmine could put in the mug, in litres? Assume she can fill the mug
right to the top.
c) What is the surface area of the outside of the mug?
2. Davon is a wedding decorator. She is preparing cylindrical vases filled with coloured sands to place as
centrepieces on the tables. She has 12 vases. Each vase is 1.3 feet high with a diameter of 4 inches.
a) What is the total volume of all 12 vases?
b) Davon wants to fill 75% of the volume with purple sand and the remaining volume with pink sand. How
many gallons of each colour of sand does she need? (There are 231 in3 per US gallon.)
c) The purple sand comes in 1.5 gallon bags. How many bags of purple sand will she need to purchase?
3. A delicate glass tube is being delivered to a school science lab. The tube is 60 cm long with a radius of 0.75 cm.
It is being shipped in a cylindrical container with a length of 70 cm and a radius of 2.25 cm.
a) Draw and label a diagram of the shipping container.
b) Calculate the volume between the shipping container and the glass tube, which will be filled with sawdust
to protect the tube. Give your answer in litres.
4. Samir is managing a berry farm for the summer. Berry pickers empty their baskets into a cylindrical bin with a
radius of 4 feet and a height of 11 feet. The silo is currently
full.
a) What is the maximum capacity, in US gallons, of the silo? (1 ft3 = 7.48 US gallons)
b) How many more gallons of berries need to be picked to fill the bin?
c) If one gallon of these berries weighs 12.7 pounds, how many pounds of berries have already been collected?
5. a) Find the volume of the oblique rectangular prism shown.
6m
8m
7m
b) If the height of the prism is tripled, how many times larger does the volume become? Express your answer
as a percentage.
6. A cylindrical hot water tank has a radius of 1.4 feet and a height of 6.5 feet.
a) How much water, in US gallons, does the tank hold? There are 7.48 US gallons in a cubic foot.
b) If it heats water at a rate of 13 gallons/2 min, how long will it take to heat all the water in the tank if it is full?
7. A cone has a radius of 50 cm and a height of 17 cm.
a) What is its volume?
b) What is its capacity, in litres?
8. A cone has a radius of 17 inches and a height of 35 inches.
a) What is its volume?
b) If all the measurements of the cone are decreased by 70%, what is the new volume?
c) What percentage of the original volume is the volume of the smaller cone?
9. A pyramid-shaped grain storage funnel is 8 m wide, 11 m long, and has a height of 12 m m.
a) Draw a diagram of the funnel and label the dimensions.
b) What is the volume of the funnel?
c) If the funnel is 50% full, how many litres of grain is it holding?
10. A spherical water tower has an outer radius of 17 feet.
a) What is the volume of the water tower?
b) If the wall of the water tower is 0.5 feet thick, what will be the capacity, in US gallons, of the water tower?
There are 7.48 US gallons in a cubic foot.
11. A mould is being made to make spherical plastic pieces. The mould will be rectangular and will be made out of
steel. It will be made in two halves, so that the spheres can be drilled into the steel, then the two halves will be
joined together to form a block. The outer dimensions of the steel block are as shown in the diagram.
0.6 m
0.6 m
2.2 m
a) There must be at least 20 cm of steel around each plastic sphere in the mould. If each sphere will have a
diameter of 0.2 m, how many spherical holes can be made in this mould?
b) What volume of steel in litres is required to create the mould?