Non-Calculus Physics Question?

Question

A spherical balloon is partially blown up and its surface area is measured. More air is then added, increasing the volume of the balloon. If the surface area of the balloon expands by a factor of 9.1 during this procedure, by what factor does the radius of the balloon change?

Answer 1

Surface area of a balloon (sphere) = 4(pi)r^2

where

r = radius of the balloon

If the surface area increases by a factor of 9.1, then the new surface area becomes

9.1S = 4(pi)R^2

where R = corresponding radius of the increased balloon size

Comparing the two surface areas,

(9.1S/S) = [4(pi)R^2]/[4(pi)r^2]

R^2/r^2 = 9.1

R^2 = 9.1r^2

R = 3.02r

The new radius is 3.02 times bigger than the previous one.