Question

If the radius of a sphere is increased by 50%, then the ratio of the percentage increase in
volume to the percentage increase in the surface area of the sphere is​

Answer 1

Let the original radius be r.

So, the surface area of the sphere =4πr2             .......(1)


Since, the radius is increased by 50%, then

The new radius =1.5r


Therefore, the new surface area of the sphere will be

=4π(1.5r)2

=2.25×4πr2                .........(2)


Therefore, the required percentage

=4πr22.25×4πr2−4πr2​×100

=4πr2h1.25×4πr2h​×100

=125%


Hence, this is the answer.