Practice Surface Area in Math

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

Quick Recap

The total area of all the faces or surfaces that enclose a three-dimensional object, measured in square units.

How much wrapping paper would you need to completely cover every face of a gift box?

Showing a random 20 of 50 problems.

Example 1

medium
A cube has surface area 9696. What is its volume?

Example 2

hard
A cylinder is inscribed in a cube of edge 66 (so it just fits, tangent to all four side faces). Find the lateral surface area of the cylinder in terms of ฯ€\pi.

Example 3

medium
A cube of side 44 is painted, then cut into unit cubes. Two opposite faces' worth of painted area โ€” what is the total painted surface area of the original cube?

Example 4

easy
Find the total surface area of a square pyramid with base side 44 and slant height 66.

Example 5

easy
Find the surface area of a cube with side 22 cm.

Example 6

medium
Find the surface area of a cylinder with radius 44 cm and height 77 cm. Leave your answer in terms of ฯ€\pi.

Example 7

easy
Find the surface area of a rectangular box with length 55, width 44, height 22.

Example 8

medium
A closed cylinder has radius 22 cm and height 1010 cm. Find its surface area in terms of ฯ€\pi.

Example 9

easy
Two cubes have edge lengths 22 and 55. What is the ratio of their surface areas?

Example 10

medium
Find the surface area of a cylinder with radius 33 and height 55 (in terms of ฯ€\pi).

Example 11

challenge
Why does a small animal lose body heat faster than a large one, in terms of surface-area-to-volume ratio?

Example 12

easy
Find the surface area of a cube with side 11.

Example 13

hard
A cylinder has the same surface area as a cube with edge 66. If the cylinder has radius 33, find its height in terms of ฯ€\pi.

Example 14

medium
A cube has surface area 150150 cmยฒ. Find the length of one edge.

Example 15

medium
Find the surface area of a cube whose space diagonal is 75\sqrt{75}.

Example 16

medium
A hemisphere has radius 44. Find its total surface area (curved surface + flat disk) in terms of ฯ€\pi.

Example 17

medium
Find the surface area of a sphere with radius 33 (in terms of ฯ€\pi).

Example 18

easy
Which uses square units: the amount of paint to cover a ball, or the air inside it?

Example 19

challenge
A cube and a sphere both have surface area SS. Show which encloses more volume, and name the principle.

Example 20

easy
Find the surface area of a rectangular prism with length 44 cm, width 33 cm, and height 55 cm.