posted by yohannes .
The radius of sphere at therate of 4cm per second .at what ratis its surface area chang when theradius is 6cm
You seem to have left out some words in your question, such as:
The radius of sphere IS INCREASING at the rate of 4cm per second.
Surface area is
The rate of increase of surface area is
dA/dt = 8*pi*R*(dR/dt)
Plug in 6 cm for R, and dR/dt = 4 cm/s, and compute
dA/dt = 64πt²=128 πt=128 π•1.5=603.2 cm²/s