The volume of a sphere is increasing at the rate of 5 cm.cm.per second .Find the rate of increase of the radious and surface area when the radious is 6cm.
V = (4/3)π r^3
dV/dt = 4π r^2 dr/dt
when r = 6, dV/dt = 5
5 = 4π (25) dr/dt
dr/dt = 5/(100π) = 1/(20π) cm/s
A = 4π r^2
dA/dt = 8π r dr/dt
= 8π(5)(1/100π )
= 2/5 cm^2 /s