The volume of a sphere is increased by 6% calculate the corresponding percentage increase in the area.

Answer 1

volume would be proportional to the cube of the radius

so original radius =(1.06)^(1/3)

But area is proportional to the square of the radius

so new area = ( (1.06)^(1/3) )^2
= 1.06^(2/3)
= 1.0396

so the surface area increased by appr 3.96%