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 60 mm? evaluate your answer numerically. (round the answer to the nearest whole number.)

Answer 1

The diameter of the sphere is 60 mm which means its radius is 30mm. The radius of a sphere is increasing at a rate of 5 mm/s. 
The formula for the radius when the time is x second would be:
r(t)= 30+ 5x
dr/dt= 5

The speed of volume increase of the sphere volume would be derived from sphere volume: 
V(r)=4/3* pi * r^3
dV/dt= 4/3 * pi * 3r^2 * (dr/dt) =4/3* pi * 3(30)^2 * 5 =  18000 pi= 56571 mm^3/s