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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