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Question

If the diameter of a sphere is decreased by 25%, then its curved surface area decreases by

A
44.25%
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B
43.50%
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C
43.75%
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D
75.43%
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Solution

The correct option is C 43.75%

Let the original diameter of the sphere be 2x.
Then, original radius of the sphere = x
Original curved surface area = 4πx2
Decreased diameter of the sphere
=2x25% of 2x
=2xx2=32x
Decreased radius of the sphere = 34x
Decreased curved surface area
=4π(34x)2=94πx2
Decrease in area=4πx294πx2=74πx2
Hence, percentage decrease in area
=74πx24πx2×100%
=716×100%=1754%=43.75%


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