Question

Helium is pumped into a spherical balloon at a constant rate of 4 cubic feet per second. How fast is the radius increasing after 3 minutes.At what time is the radius increasing at a rate of 100 feet per second?

Answer 1

V = (4/3)*pi*r^3

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

Answer 2

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

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

Answer 3

ok i got that

Answer 4

PLEASE HELP ME IM REALLY STUCK!!!!!!!!!

Answer 5

The volume of a sphere is:

V = (4/3)πr^3.

By implicit differentiation:

dV/dt = 4πr^2(dr/dt).

We know dV/dt and wish to find dr/dt. In order to find dr/dt, we also need to know r. After 3 minutes. Notice that 3 minutes = 180 seconds. Then, after 3 minutes, the volume of the balloon is 180(3) = 540 cubic feet. At this point:

540 = (4/3)πr^3, by substituting V = 540
==> r = (405/π)^(1/3).

Therefore:

dV/dt = 4πr^2(dr/dt)
==> dr/dt = (dV/dt)/(4πr^2)
= 3/[4π(405/π)^(2/3)]
≈ 0.0094 ft/s.

Answer 6

Hope this helps.

Answer 7

but i have an answer and its telling me it is 0.0103 ft./sc and i dont know how to get it

Answer 8

Just follow the formula I gave you and you should find it.

Answer 9

is there any other info... like r(t) = ???

Answer 10

double check to see if they give a formula for the radius, r(t) = ???

Answer 11

hello?

Answer 12

no

Answer 13

you have to find r

Answer 14

helium is pumped into a spherical balloon ar a constant rate of 4 cubic feet per second. How fast is the radius increasing after 3 minuites?

Answer 15

at what time(if any) is the radius increasing at a rate of 100 ft per second?

Answer 16

I believe that the 180(3) in the @TurtleNadz post above (the long post) should be 180(4) for 720 for volume, and then calculate r