# Volume of a Three-Dimensional Figure on the ISEE

#### All Levels

**ISEE Lower-Level Volume Question:**

The side length of a cube is 4 centimeters. What is its volume?

A) 16 cm^{3}

B) 32 cm^{3}

C) 64 cm^{3}

D) 96 cm^{3}

**The solution:** V *cube* = s^{3}

By definition, the length, width, and height of a cube are all equal. The volume of a cube is its side length cubed, or s x s x s. In this case, 4 × 4 × 4 = 64. **The volume of the cube is 64 cm ^{3}, answer choice C.**

**ISEE Middle-Level Volume Question:**

The dimensions of a rectangular box are 5 in. by 10 in. by 1 foot. What is the volume of the box?

A) 50 in^{3}

B) 300 in^{3}

C) 500 in^{3}

D) 600 in^{3}

**The solution:** V *rectangular prism* = l x w x h

Use the formula for volume of a rectangular prism: **length X width X height**

Step 1: Make sure all your dimensions are in the same unit, converting units as necessary.

1 *foot* x = 12 *in.*

**Helpful tip:** The ISEE will sometimes give you two different units in a problem. Make sure to convert everything to the same unit before you multiply and/or before you choose the correct answer.

Step 2: Multiply length by width by height.

5 × 10 × 12 = 600

**The correct answer is D) 600 in ^{3}**

**Helpful tip:** To find the volume of any three-dimensional prism or cylinder, use the formula: Volume = (area of the base) x height

For example, if we know that the radius of a cylinder is 5 and the height is 7, the formula for the volume of the cylinder would be: V *cylinder* = πr^{2}h = π x 5^{2} x 7 = 175π