A spherical balloon expands when it is taken from the cold outdoors into a warm house. If the surface area increases by 50% (factor of 1.50), by what percentage does the radius of the balloon change?

Question

a)7.7%
b)50%
c)100%
d)75%
e)22%

Answer 1

radius is proportional the square root of area.

R2/R1 = sqrt(A2/A1)

relaive change = (R2 - R1)/R1
= (R2/R1) - 1

sqrt(1.50) - 1 = 0.2247 = 22.47%