Question

A snowball melts so that its volume decreases at a rate of 1 cm^3/min. find the rate at which the radius is changing when the diameter is 6 cm.

Answer 1

V=(4/3)*pi*r^3
(dv/dt)=4*pi*r^2*(dr/dt)
(dv/dt)=-1cm^3/sec
-1=4*pi*r^2(dr/dt)
r=d/2=6/2=3
-1=4*pi*3^2*(dr/dt)
(dr/dt)=-1/(36*pi)
=-.087266 cm/s