Answer: The radius increases by 0.032 cm/minute.
Explanation:
The volume, V, of a sphere is V = (4/3)πr^3.
For the volume to increase at a rate of 10cc (cubic centimeters) per minute, the radius must increase such that the additional radius (r)^3 = 10
V = (4/3)πr^3
V = (4/3)π5^3
V = 524 cc
We add 10 cc to have the balloon hold 544 cc. We calculate the increase in radius:
534=(4/3)*pi*x^3
We can now calculate the new radius, x.
x = 5.032 cm
The radius increased by 0.032 cm/minute.