Question

Find the rate of increase (with respect to r) in the surface area (S=4πr2) of a spherical balloon when:
(A) r=2 inches → Rate of increase =

(B) r=4 inches → Rate of increase =

(C) r=6 inches → Rate of increase =

Answer 1

rate of change = first derivative

since we are findign the rate of change with respect to radius,
we find \(\displaystyle {dS\over dr}\)

Answer 2

what will be the derivative?

Answer 3

S = 4pi*r^2

dS/dt = 4pi*2*r*dr/dt

Answer 4

not with "t"
just with "r"

Answer 5

there is no variable "t" in the system.
the question said .. with respect to radius (r)

Answer 6

ok so what do i need to do?

Answer 7

@electrokid

Answer 8

\[
{dS\over dr}=4\pi(2r)=8\pi r
\]

Answer 9

this is what is asked

Answer 10

ok so the answer is 8pi r

Answer 11

yep.
that is the rate of increase of S with respect to r

Answer 12

ok, thank you so much

Answer 13

yw