Question : If the radius of a sphere is doubled, then its surface area will be increased by:
Option 1: 100%
Option 2: 200%
Option 3: 300%
Option 4: 400%
Correct Answer: 300%
Solution :
Given that the radius of a sphere is doubled.
Let initial radius = $r_0$
We know that the surface area of a sphere = $4\pi r^2$
⇒ Initial surface area = $4\pi r_0^2$
Now, final radius = $2r_0$
⇒ Final surface area =$4\pi(2r_0)^2$
= $4×4\pi r_0^2$
= $16\pi r_0^2$
Increase in surface area = $16πr_0^2-4\pi r_0^2$
= $12\pi r_0^2$
Percentage increase in surface area = $\frac{12\pi r_0^2}{4\pi r_0^2}\times 100$ = 300%
Hence, the correct answer is 300%.
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