ACT Math : How to find the volume of a polyhedron

Study concepts, example questions & explanations for ACT Math

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Example Questions

Example Question #11 : Solid Geometry

In cubic feet, find the volume of the pentagonal prism illustrated below. The pentagon has an area of , and the prism has a height of \displaystyle 8\textup{ft}.

4

Possible Answers:

\displaystyle 224\textup{ft}^{3}

\displaystyle 128\textup{ft}^{3}

\displaystyle 20\textup{ft}^{3}

\displaystyle 96\textup{ft}^{3}

Correct answer:

\displaystyle 128\textup{ft}^{3}

Explanation:

For any prism, the volume is given by the following equation:

\displaystyle \text{Volume}=\text{Area of base}\times\text{height}

The question gives us the area of the base and the height.

\displaystyle \text{Volume}=16\times8=128

Example Question #11 : Other Polyhedrons

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

Possible Answers:

The volume will be \displaystyle 27 times as large.

The volume will be \displaystyle 9 times as large.

The volume will be \displaystyle 3 times as large.

The volume will be \displaystyle 8 times as large.

Correct answer:

The volume will be \displaystyle 27 times as large.

Explanation:

Start by taking a cube that is \displaystyle 1\times1\times1. The volume of this cube is \displaystyle 1.

Next, triple the sides of this cube so that it becomes \displaystyle 3\times3\times3. The volume of this cube is \displaystyle 27

The volume of the new cube is \displaystyle 27 times as large as the original.

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