physics
posted by yohannes on .
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
A= 4*pi*R^2
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 
R=4t (cm)
6=4t
t=1.5 s.
A=4πR²=4π(4t)²=
=64πt²=64π(1.5)²=452.4 cm² 
dA/dt = 64πt²=128 πt=128 π•1.5=603.2 cm²/s