### Volume – Geometric Shapes

The ACT math test will have questions that ask you to calculate the volume of certain geometric shapes.

You may need to do these types of calculations for a cylinder, cone, or box on the examination.

If you do not know the formulas for these concepts, be sure to check our **ACT Math Cheat Sheet** before you attempt the problems below.

**Problem 1:**

A box is manufactured to contain either laptop computers or notebook computers. When the computer systems are removed from the box, it is reused to hold other items.

If the length of the box is 20cm, the width is 15cm, and the height is 25cm, what is the volume of the box?

A. 150

B. 300

C. 750

D. 7500

E. 15000

**The correct answer is D.**

To find the answer to this problem, you need this formula:

box volume = base × width × height

Now substitute the values into the formula from the problem:

base × width × height =

20 × 15 × 25 =

7500

**Problem 2:**

Consider a cone with a height of 12 inches and a radius at its base of 3 inches. What is the volume of this cone?

F. 3π

G. 12π

H. 36π

J. 72π

K. 108π

**The correct answer is H.**

To find the answer to this problem, use this formula:

cone volume = [height × radius^{2} × π] ÷ 3

Now substitute the values from the problem.

[12 × 3^{2} × π] ÷ 3 =

36π

**Problem 3:**

What is the volume of a cylinder that has a radius of 6 and a height of 10?

A. 36π

B. 360π

C. 12π

D. 120π

E. 600π

**The correct answer is B.**

To find the answer to this problem, use this formula:

cylinder volume = height × radius^{2} × π

Now substitute the values from the problem.

[10 × 6^{2} × π] =

360π

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