How to find the volume of a polyhedron

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SSAT Upper Level Quantitative › How to find the volume of a polyhedron

Questions 1 - 10
1

Find the volume of a prism that has a right triangle base with leg lengths of and and a height of .

Explanation

To find the volume of a prism, multiply the area of the base by the height.

2

Find the volume of a square pyramid that has a height of and a side length of .

Explanation

The formula to find the volume of a square pyramid is

So plugging in the information given from the question,

3

Find the volume of a square pyramid with a height of and a length of a side of its square base of .

Explanation

The formula to find the volume of a square pyramid is

So plugging in the information given from the question,

4

Find the volume of a regular hexagonal prism that has a height of . The side length of the hexagon base is .

Explanation

The formula to find the volume of a hexagonal prism is

Plugging in the values given by the question will give

5

Find the volume of a regular hexagonal prism that has a height of . The side length of the hexagon base is .

Explanation

The formula to find the volume of a hexagonal prism is

Plugging in the values given by the question will give

6

In terms of , find the volume of a regular hexagonal prism that has a height of . The hexagon base has side lengths of .

Explanation

The formula to find the volume of a hexagonal prism is

Plugging in the values given by the question will give

7

Find the volume of a regular tetrahedron that has side lengths of .

Explanation

The formula to find the volume of a tetrahedron is

Plugging in the information given by the question gives

8

Find the volume of a regular tetrahedron with a side length of .

Explanation

The formula to find the volume of a tetrahedron is

Plugging in the information given by the question gives

9

Find the volume of a regular octahedron that has a side length of .

Explanation

Use the following formula to find the volume of a regular octahedron:

Plugging in the information from the question,

10

Find the volume of a regular octahedron that has a side length of .

Explanation

Use the following formula to find the volume of a regular octahedron:

Plugging in the information from the question,

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