Question

The diameter of a sphere is decreased by 25%. By what percent does its curved surface area decrease?

A. 63.75 %
B. 43.95 %
C. 73.75 %
D. 43.75 %

Answer 1

D. 43.75%

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The curved surface area of a sphere is given by the formula:

• A = 4πr², where r is the radius

Since the diameter is decreased by 25%, it means the new diameter is 75% of the original. Therefore, the new radius will also be 75% of the original radius.

Let's calculate the new curved surface area:

• A(new) = 4π(0.75r)² = 4π(0.5625r²) = 0.5625 * (4πr²) = 0.5625*A

This means that the curved surface area decreases by:

• (1 - 0.5625) = 0.4375 = 43.75%