How to find the volume of a polyhedron

Practice Questions

ACT Math › How to find the volume of a polyhedron

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1

A cube has a surface area of . What is its volume?

2

A pyramid is placed inside a cube so that they share a base and height. If the surface area of the cube is , what is the volume of the pyramid, in square feet?

3

Roberto has a swimming pool that is in the shape of a rectangular prism. His swimming pool is meters wide, meters long, and meters deep. He needs to fill up the pool for summer, and his hose fills at a rate of cubic meters per hour. How many hours will it take for Roberto to fill up the swimming pool?

4

Susan bought a chocolate bar that came in a container shaped like a triangular prism shown below. If the container is completely filled with chocolate, in cubic inches, what volume of chocoate did Susan buy?

3

5

The tent shown below is in the shape of a triangular prism. What is the volume of this tent in cubic feet?

2

6

The height of a box is twice its width and half its length. If the volume of the box is , what is the length of the box?

7

If the side lengths of a cube are tripled, what effect will it have on the volume?

8

Matt baked a rectangular cake for his mom's birthday. The cake was inches long, inches wide, and inches high. If he cuts the cake into pieces that are inches long, inches wide, and inches high, how many pieces of cake can he cut?

9

In cubic inches, find the volume of a tetrahedron that has a surface area of .

10

Troy's company manufactures dice that are shaped like cubes and have side lengths of . If the plastic needed to make the dice costs per cubic centimeter, how much does it cost Troy to make one die?

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