# SSAT Upper Level Math : How to find the volume of a polyhedron

## Example Questions

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### Example Question #1 : How To Find The Volume Of A Polyhedron

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,

### Example Question #2 : How To Find The Volume Of A Polyhedron

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,

### Example Question #27 : Volume Of A Three Dimensional Figure

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

### Example Question #4 : How To Find The Volume Of A Polyhedron

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

### Example Question #1 : How To Find The Volume Of A Polyhedron

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

### Example Question #2 : How To Find The Volume Of A Polyhedron

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,

### Example Question #3 : How To Find The Volume Of A Polyhedron

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,

### Example Question #4 : How To Find The Volume Of A Polyhedron

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

Explanation:

A regular hexahedron is another name for a cube.

To find the volume of a cube,

Plugging in the information given in the question gives

### Example Question #5 : How To Find The Volume Of A Polyhedron

Find the volume of a regular octahedron with side lengths of .

Explanation:

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

Plugging in the information from the question,

### Example Question #6 : How To Find The Volume Of A Polyhedron

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