IXL | Relate between volume and surface area

The surface area of this rectangular prism is 190 square millimeters. What is the volume?

9 mm

7 mm

volume = cubic millimeters

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question

The surface area of this rectangular prism is 58 square feet. What is the volume?

4 ft

5 ft

volume = cubic feet

key idea

A rectangular prism has 3 pairs of identical faces. Each face is a rectangle.

Volume = length × width × height

solution

Find the area of the faces in each pair.

4 × t = 4t

t × 5 = 5t

5 × 4 = 20

Add the areas of the 6 faces to find the surface area.

4t + 4t + 5t + 5t + 20 + 20

18t + 40

Now solve for t.

58 − 40

18t

The rectangular prism is 1 foot wide. Now you know the length, width, and height.

length: 4 ft
width: 1 ft
height: 5 ft

Use these numbers in the volume formula.

Volume

length × width × height

4 × 1 × 5

The volume is 20 cubic feet.

Looking for more? Try these:

Lesson: What is surface area?

Lesson: Volume of rectangular prisms

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Teacher tools

Work it out

Not feeling ready yet? These can help:

CC.1Surface area of cubes and prisms

CC.5Volume of cubes and prisms

Lesson: What is surface area?

Lesson: Volume of rectangular prisms

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