Q.If the radius of a sphere is doubled, by what percentage does its curved surface area increase?

Let the radius of the sphere initially be \(r\) units. Then the new radius becomes \(2r\) units.
The original curved surface area of the sphere: \[ = 4\pi r^2 \ \text{square units} \] New curved surface area: \[ = 4\pi (2r)^2 = 4\pi \times 4r^2 = 16\pi r^2 \ \text{square units} \] Increase in area: \[ = 16\pi r^2 - 4\pi r^2 = 12\pi r^2 \ \text{square units} \] Percentage increase: \[ = \frac{12\pi r^2}{4\pi r^2} \times 100 = 300\% \] (ANSWER)
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