Question

The radius of a sphere is increasing at a rate of 4 mm/s. How fast is the volume increasing when the diameter is 60 mm?

Answer 1

V = [4/3]π r^3 => [dV / dr ] = 4π r^2

[dV/dt] = [dV/dr] * [dr/dt]

[dV/dt] = [4π r^2] * [ dr/ dt]

r = 60 mm, [dr / dt] = 4 mm/s

[dV / dt ] = [4π(60mm)^2] * 4mm/s = 180,955.7 mm/s