Do you get the square root for the volume of a sphere?

The surface area is proportional to the square of the radius, so if we have increased the surface area by 25% (multipled by 1.25) then we have increased the radius by sqrt (1.25). This is because the radius increases as the square root of the surface area. Now the volume increases as the cube of the radius and the radius has increased by sqrt (1.25) so the volume has increased by (sqrt (1.25)) ^3 which is roughly 40%.