Volume Word Problems Practice Questions

To review these concepts, go to Volume Word Problems Study Guide.

Volume Word Problems Practice Questions

Practice 1

Problems

1. What is the volume of a rectangular prism with a length of 5 m, a width of 6 m, and a height of 12 m?
2. What is the height of a rectangular prism with a length of 10 in., a width of 3 in., and a volume of 210 in.²?
3. What is the volume of a cube with an edge that measures 4 cm?
4. What is the volume of a triangular prism with a height of 6 ft. and a base area of 14 ft.²?
5. What is the volume of a square base pyramid with a base area of 18 m²and a height of 8 m?

Solutions

1. Read and understand the question. This question is looking for the volume of a rectangular prism when the three dimensions are given.

Make a plan. Use the formula V = l × w × h and substitute the given values.

Then, evaluate the formula.

Carry out the plan. The volume is V = 5 × 6 × 12 = 360 m³.

Check your answer. To check this solution, divide the volume by two of the dimensions to check if the result is the third dimension.

360 ÷ 5 = 72
72 ÷ 6 = 12

which is the remaining dimension. This solution is checking.

2. Read and understand the question. This question is looking for the height of a rectangular prism when the volume and two dimensions are given.

Make a plan. Use the formula V = l × w × h and substitute the given values.

Then, evaluate the formula.

Carry out the plan. The formula becomes 210 = 10 × 3 × h. Multiply to get 210 = 30h. Divide each side of the equation by 30 to get h = 7. The height is 7 in.

Check your answer. To check this solution, multiply the dimensions to check if the result is the volume.

V = 10 × 3 × 7 = 210

This solution is checking.

3. Read and understand the question. This question is looking for the volume of a cube when the measure of an edge of the cube is known.

Make a plan. Use the formula V = e³and substitute the given value of e.

Then, evaluate the formula.

Carry out the plan. The volume formula becomes V = (4)³= 4 × 4 × 4 = 64 cm³.

Check your answer. To check this solution, divide the volume by the measure of the edge of the cube two times to see if the result is also the measure of the edge.

64 ÷ 4 = 16
16 ÷ 4 = 4

which is the measure of the edge of the cube. This solution is checking.

4. Read and understand the question. This question is asking for the volume of a triangular prism when the area of the base and the height of the prism are given.

Make a plan. Use the formula V = Bh, where B is the area of the base and h is the height of the prism. Substitute the known values and evaluate the formula.

Carry out the plan. The formula becomes V = 14 × 6 = 84. The volume is 84 ft.³.

Check your answer. To check this problem, divide the volume of the prism by the height and check to see if the result is the area of the base: 84 ÷ 6 = 14, which is the area of the base. This answer is checking.

5. Read and understand the question. This question is looking for the volume of a square base pyramid when the area of the base and the height of the pyramid are known.

Make a plan. Use the formula V = Bh, where B is the area of the base and h is the height of the pyramid. Substitute the values and evaluate the formula.

Carry out the plan. The formula becomes

V = (18)(8) = (144) = 48

The volume is 48 cm³.

Check your answer. To check your answer, work backward. Multiply the volume by 3, and then divide by one of the dimensions to check to see if the result is the other dimension:

48 × 3 = 144
144 ÷ 18 = 8

This result is checking.