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.
a. 32pi
b. 16pi
c. 64pi
d. 4pi

Answer 1

@eliassaab

Answer 2

@iambatman @TuringTest @Abhisar @SolomonZelman @iGreen

Answer 3

@iGreen please help

Answer 4

@eliassaab

Answer 5

@Brostep0s

Answer 6

will give medal

Answer 7

Idk

Answer 8

please, you have to calculate the first derivative oS with respecto to r, first, namely:
\[\frac{ dS }{ dr }=...\]

Answer 9

@Michele_Laino how would one do tht

Answer 10

what is the first derivative of r^2 with respect to r^

Answer 11

we have:
\[\frac{ dS }{ dr }=\frac{ d (4 \pi r ^{2}) }{ dr }=8 \pi r\]
do you agree?

Answer 12

ya

Answer 13

so insert 4 into r and get 32pi?

Answer 14

that's right!