55967
AssignmentMultiple Choice

Spheres

Question 55967 • Reading HS- Integrated Math I

A company manufactures exercise balls for gyms. Type A is a spherical ball with a radius of 12 inches. Type B is a hemisphere that will remain stationary when placed on its base. The radius of the hemisphere is also 12 inches. What is the ratio of the surface area of the sphere to the surface area of the hemisphere?

Answer
A
2 : 1
B
3 : 1
C
3 : 2
D
4 : 3

Explanation

A sphere’s surface area is 4πr². A hemisphere resting on its base has both its curved surface and its circular base, so its total surface area is 2πr² + πr² = 3πr². With the same radius, the ratio is 4πr² : 3πr² = 4 : 3, so the answer is D, 4 : 3.

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