Question

The radius of a sphere is doubled. Find the percentage increase in its surface area.

Answer 1

Given that the radius of a sphere is doubled.

To find out; Percentage increase in its surface area.

Let initial radius $=r_0$

We know that the surface area of a sphere $=4\pi r^2$.

Hence, initial surface area $=4\pi r_0^2$

Now, final radius $=2r_0$

Hence, final surface area $=4\pi (2r_0{)}^2$

$=4\times 4\pi r_0^2$

$=16\pi r_0^2$

Hence, increase in surface area $=16\pi r_0^2-4\pi r_0^2=12\pi r_0^2$

So, percentage increase in surface area $=\frac{12\pi r_0^2}{4\pi r_0^2}\times 100=300\%$.

Hence, if the radius of a sphere is doubled, its surface area increases by $300\%$.