Proving dr/dt

[Mel Mitch]

Hello..........I'm lost

Prove that dr/dt= 3/(4 (pi) r^2).....If the following is given:

The volume (V) of a sphere of a radius( r )= ______ and the surface area(A)_____.
(I) The Volume is increasing at a steady rate of 3cm^3/s and t is time in seconds.

I know that V= 4/3 (pi)r^3
and A= 4(pi) r^2

so how do i go about finding dr/dt?????

(ii) find da/dt??????

 

[arthur ohlsten]

V=4/3 pi r^3

dV/dt=4 pi r^2 dr/dt
dr/dt = dV/dt / {4 pi r^2]
but dv/dt = 3 [cm^3/s]

dr/dt= 3/[4pir^2] cm/s r in cm
Arthur

 

[Mel Mitch]

thanks arthur ohlsten
i see it now
dv/dt= dv/dr .dr/dt and just change the subject of the formula

hence da/dt= da/dr . dr/dt

thanks again