Question

The radius r of a sphere is increasing at a rate of 9 inches per minute.
(a) Find the rate of change of the volume when r = 10 inches.

.......... in.3/min

(b) Find the rate of change of the volume when r = 36 inches.

.............. in.3/min

Answer 1

But this is not the right answer for some reason can someone help me?

Answer 2

Related rates, so what did you try?

Answer 3

Volume of a sphere is \[V = \frac{ 4 }{ 3 } \pi r^3\] and we know \[\frac{ dr }{ dt } = 9 \frac{ i n }{ \min }\]

Answer 4

We need to find dV/dt

Answer 5

yes i got to the point where

dV/dt = 4 pi r ^2 (dR/dt)

Answer 6

and then put in the numbers and got 3600 but it isn't right

Answer 7

\[\frac{ dV }{ dt } = 4 \pi r^2 \frac{ dr }{ dt } \implies 4 \pi (10i n)^2(9) = 3600 \pi \frac{ i n^3 }{ \min }\]

Answer 8

oh
lol thanks

Answer 9

forget pi? :P

Answer 10

yeah

Answer 11

:)

Answer 12

Same process with r = 36

Answer 13

yep thanks