Rates of Change (1 Viewer)

[Aesytic]

The volume of a sphere is increasing at a rate numerically equal to its surface area at that instant. Show that dr/dt = 1

I thought this would be quite straightforward, and it might, but I don't really have any idea as to where to start :/

 

[bleakarcher]

V=(4/3)pi*r^3
dV/dr=4pi*r^2
dV/dt=4pi*r^2=(dr/dt)*(dV/dr)=(dr/dt)*(4pi*r^2)
i.e. (dr/dt)*4pi*r^2=4pi*r^2
=>dr/dt=1 as requested.

 

[Aesytic]

i misread the question and thought it meant the rate of change of the surface area as well -.-
thanks bleakarcher!