Question

CALCULUS DERIVATIVES: Air is being released from a spherical balloon at the rate of 3 cu. in./min. What is the rate of change of the radius of the balloon when the radius of the balloon is 2 in.?

Answer 1

So, I need to find dr/dt right?

Answer 2

V = 4pi/3*r^3

dV/dt = dV/dr * dr/dt

dV/dt = 4pi/3 * 3 * r^2 * dr/dt

Answer 3

why v=4pi/3&r^3?

Answer 4

Doesn't v= 4/3 *pi *r^3 ?

Answer 5

thats the same thing

Answer 6

4pi/3 = 4/3 * pi

Answer 7

ohh yeah ok

Answer 8

so dr/dt= 3/16pi ?

Answer 9

we have to be careful

Answer 10

We have to rationalize?

Answer 11

my draw button is frozen :/

Answer 12

ok did you get
dV/dt = 4pi* r^2 * dr/dt

Answer 13

Air is being released from a spherical balloon at the rate of 3 cu. in./min. What is the rate of change of the radius of the balloon when the radius of the balloon is 2 in.?

dV/dt = -3
r= 2

-3 = 4pi* (2)^2 * dr/dt

Answer 14

so the 3's cancel out

Answer 15

right

Answer 16

ok