Question

The radius of a sphere is increasing at a rate of 3 mm/s how fast is the volume increasing when the diameter is 100 mm

Answer 1

dr/dt = 3mmps

now,

d(4/3*pi*r^3)/dt = 4/3*pi*3r^2*dr/dt

= 4/3*3.14*3(100)^2*3 cubicmmps approx