Practice Sphere Surface Area in Math

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

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Quick Recap

The total area covering the curved outer surface of a sphere, given by the formula S=4Ο€r2S = 4\pi r^2.

The 'skin area' of a perfectly round ballβ€”the amount of material needed to cover it with no overlaps.

Showing a random 20 of 50 problems.

Example 1

hard
A spherical tank has surface area 400Ο€400\pi ft2^2. How many gallons does it hold? (1 ft3^3 β‰ˆ7.48\approx 7.48 gal.)

Example 2

medium
Why does a sphere have the smallest surface area for a given volume?

Example 3

easy
Find the surface area of a sphere with radius 44 in terms of Ο€\pi.

Example 4

challenge
A sphere and a cube have equal surface areas. The sphere has radius 3. Find the cube's edge length (use Ο€β‰ˆ3.14\pi \approx 3.14).

Example 5

easy
What is the formula for the surface area of a sphere?

Example 6

medium
Spherical bearing has surface area 16Ο€16\pi mm2^2. What is its diameter?

Example 7

medium
Two spheres have radii 3 and 6. Find the ratio of their surface areas.

Example 8

easy
Find the surface area of a sphere with radius 77 cm.

Example 9

challenge
Why do small water droplets form near-perfect spheres, in terms of surface area and energy?

Example 10

easy
If a sphere's radius doubles, its surface area multiplies by what factor?

Example 11

easy
Find the surface area of a sphere with radius 3 in terms of Ο€\pi.

Example 12

hard
If a sphere's radius increases by 50%50\%, by what percent does its surface area increase?

Example 13

hard
Two spheres have radii in the ratio 2:32:3. Find the ratio of their surface areas. If the smaller sphere has a surface area of 64Ο€64\pi cmΒ², find the surface area of the larger sphere.

Example 14

easy
Find the curved surface area of a hemisphere with radius 88, in terms of Ο€\pi.

Example 15

easy
Find the surface area of a sphere with radius 5 in terms of Ο€\pi.

Example 16

medium
A sphere has a surface area of 100Ο€100\pi cmΒ². Find its radius and volume.

Example 17

medium
A sphere has surface area SS. Express its radius in terms of SS.

Example 18

easy
A basketball has a diameter of 2424 cm. Find its surface area.

Example 19

medium
A sphere has surface area 144Ο€144\pi. Find its volume in terms of Ο€\pi.

Example 20

medium
A sphere is inscribed in a cube of side 8. Find the sphere's surface area in terms of Ο€\pi.
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