The surface area, S, of a sphere of radius r feet is S = S(r) = 4πr2. Find the instantaneous rate of change of the surface area with respect to the radius r at r = 4.

Question

superdavesuper · Answer

instantaneous rate of change of the surface area S with respect to the radius r
= dS/dr
= d(4πr2)/dr
= ...

chris215 · Answer

whats d stand for?

superdavesuper · Answer

d stands for differentiation...this is calculus right?

chris215 · Answer

yeah

superdavesuper · Answer

so u should know about how to differentiate a function like 4πr2...

chris215 · Answer

i got 16pi

superdavesuper · Answer

dats not the right ans...wuld u show ur steps plz?

chris215 · Answer

4π(4^2)=64pi/4=16pi

superdavesuper · Answer

dats not the right steps...sorry!

plz follow the ones below:

instantaneous rate of change of the surface area S with respect to the radius r
= dS/dr
= d(4πr^2)/dr
= 4π * d(r^2)/dr
= ?

radar · Answer

Don't forget that after you differentiate, substitute the value 4 for "r"

radar · Answer

Please show what you got for the dS/dr   (the derivative)

radar · Answer

Hint:  Use the "power rule"

radar · Answer

I am gonna have to run.  Good luck getting the derivative.

chris215 · Answer

8πr

superdavesuper · Answer

GREAT @chris215 yes, dS/dr = 8πr

now all u need to do is to put r=4 to find the rate of change at that point :)

chris215 · Answer

oh ok so 32pi

superdavesuper · Answer

Correct @chris215 good job! :)

chris215 · Answer

thanks so much