Question : If the radius of a sphere increases by 10%, what would be the change in the surface area of the sphere?
Option 1: 20%
Option 2: 21%
Option 3: 31%
Option 4: 25%
Correct Answer: 21%
Solution :
The surface area ($A$) of a sphere is $4\pi r^2$, where $r$ is the radius of the sphere.
If the radius increases by 10%, the new radius is $(r+0.1r) = 1.1r$
The new surface area of the sphere is then $= 4\pi (1.1r)^2 = 4\pi \times 1.21r^2 = 1.21 \times 4\pi r^2 = 1.21A$
So, the change in surface area $=\frac{1.21A-A}{A}×100 = 21$%
Hence, the correct answer is 21%.
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