Question

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.

Answer 1

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

Answer 2

whats d stand for?

Answer 3

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

Answer 4

yeah

Answer 5

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

Answer 6

i got 16pi

Answer 7

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

Answer 8

4π(4^2)=64pi/4=16pi

Answer 9

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
= ?

Answer 10

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

Answer 11

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

Answer 12

Hint: Use the "power rule"

Answer 13

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

Answer 14

8πr

Answer 15

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 :)

Answer 16

oh ok so 32pi

Answer 17

Correct @chris215 good job! :)

Answer 18

thanks so much