Question

A spherical balloon is being inflated at a rate of 10 cubic centimeters per second.
A. Find an expression for dr/dt, the rate at which the radius of the balloon is increasing.
B. How fast is the radius of the balloon increasing when the diameter is 40 cm?
C. How fast is the surface area of the balloon increasing when the radius is 5 cm?

Answer 1

(A) v = 4/3 πr^3
dv/dt = 4πr^2 dr/dt
dr/dt = 10/(4πr^2)
now B is easy, and
(C) A = 4πr^2
dA/dt = 8πr dr/dt