Test Index

Volumes Practice Test 4

Question : 11 of 16

Marks: +1, -0

Solution:

Concept:

Surface area of a sphere depends on the square of its radius, so

S \propto r^2

Explanation:

Let the original radius be

r

New radius after a

50\%

decrease is

r' = r - 0.5r = 0.5r

Original surface area is

S = 4\pi r^2

New surface area is

S' = 4\pi (0.5r)^2 = 4\pi r^2 \times 0.25 = 0.25S

Decrease in surface area is

S - S' = S - 0.25S = 0.75S

Percentage decrease is

\frac{0.75S}{S} \times 100 = 75\%

Answer:

The surface area decreases by

75\%

, so the correct option is D.

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