Question

The radius of a sphere is increasing at a rate of 5 mm/s. How fast is the volume increasing when the diameter is 100 mm?

Answer 1

157,143 mm/s

Explanation:

Formula for the volume of a sphere is;

V = 4/3 * pi * r^3

dv/dr = 4 pi r^2

dv/dt = dv/dr * dr/dt

dr/dt = 5 mm/s

dr/dt = 4 * pi * r^2

r = d/2 = 100/2 = 50 mm

dr/dt = 4 * 22/7 * 50^2 = 220,000/7

dv/dr = 220,000/7 * 5 = 157,142.8571428571

Approximately 157,143 mm/s