A spherical snowball is melting in such a way that its diameter is decreasing at rate of 0.3 cm/min. At what rate is the volume of the snowball decreasing when the diameter is 17 cm.

Question

campbell_st · Answer

you need to used related rates 

$$\frac{dV}{dt} = \frac{dV}{dr} \times \frac{dr}{dt}$$

you are given dr/dt  

and the volume of a sphere is 

$$V = \frac{4}{3} \pi r^3$$

so 

$$\frac{dV}{dr} = 4\pi r^2$$

which means the rate of change in volume with respect to time is 

$$\frac{dV}{dt} = 4 \pi r^2 \times 0.3$$

find the required radius and substitute then evaluate to find the rate of change