Question : The radius of a sphere is doubled. The percentage increase in its surface area is ______.
Option 1: 75%
Option 2: 100%
Option 3: 300%
Option 4: 400%
Correct Answer: 300%
Solution :
Let the radius of the sphere be $r$ units.
So, the surface area of the sphere = $4\pi r^2$ sq. units
After doubling, the new radius = 2$r$ units
So, the new surface area = $4\pi (2r)^2=16\pi r^2$ sq. units
$\therefore$ The percentage increase = $\frac{16\pi r^2-4\pi r^2}{4\pi r^2}×100=\frac{12\pi r^2}{4\pi r^2}×100= 300\%$
Hence, the correct answer is 300%.
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