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ACT Math : How to find the volume of a polyhedron

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Example Question #11 : Solid Geometry

In cubic feet, find the volume of the pentagonal prism illustrated below. The pentagon has an area of $16\textup{ft}^{2}$ $\displaystyle 16\textup{ft}^{2}$ , and the prism has a height of $8\textup{ft}$ $\displaystyle 8\textup{ft}$ .

Possible Answers:

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

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

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

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

Correct answer:

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

Explanation:

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

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

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

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

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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 $1\times1\times1$ $\displaystyle 1\times1\times1$ . The volume of this cube is $\displaystyle 1$ .

Next, triple the sides of this cube so that it becomes $3\times3\times3$ $\displaystyle 3\times3\times3$ . 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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ACT Math : How to find the volume of a polyhedron

Study concepts, example questions & explanations for ACT Math

All ACT Math Resources

Example Questions

Example Question #11 : Solid Geometry

Example Question #11 : Other Polyhedrons

All ACT Math Resources

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