IXL | Relate between volume and surface area

The surface area of this rectangular prism is 26 square feet. What is the volume?

1 ft

6 ft

volume = cubic feet

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question

The surface area of this rectangular prism is 208 square feet. What is the volume?

4 ft

6 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 × a = 4a

a × 6 = 6a

6 × 4 = 24

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

208

4a + 4a + 6a + 6a + 24 + 24

20a + 48

Now solve for a.

208 − 48

20a

160

20a

The rectangular prism is 8 feet wide. Now you know the length, width, and height.

length: 4 ft
width: 8 ft
height: 6 ft

Use these numbers in the volume formula.

Volume

length × width × height

4 × 8 × 6

192

The volume is 192 cubic feet.

Looking for more? Try these:

Lesson: What is surface area?

Lesson: Volume of rectangular prisms

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Teacher tools

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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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