## anonymous one year ago please help asap.. water is being drained from a container which has the shape of an inverted right circular cone. the container has a radius of 6.00 inches at the top and a height of 10.0 inches. at the instant when the water in the container is 9.00 inches deep, the surface level is falling at a rate 1.2 inches per second. find the rate at which water is being drained from the container.

1. DanJS

use similar triangles to put the volume formula for the cone into a function of just height

2. DanJS

differentiate, and solve for dV/dt

3. anonymous

I have no idea what im doing on this problem or what goes where?

4. triciaal

|dw:1438102666151:dw|

5. DanJS

|dw:1438103043478:dw|

6. dan815

Do you know the formula for the volume of a cone as a function of its height V=f(h)

7. DanJS

solve for r, and put that into the volume formula so it is just in terms of h.

8. DanJS

Givens - h=9, dh/dt = 1.2

9. triciaal

and I saw this |dw:1438103242401:dw|

10. DanJS

$V = \frac{ 1 }{ 3 }\pi*r^2*h$ from similar triangles... $r = \frac{ 3 }{ 5 }h$ $V(h) = \frac{ 1 }{ 3 }\pi*(\frac{ 3 }{ 5 }h)^2*h$

11. DanJS

simplify that, then differentiate both sides w.r.t time, you are given dh/dt

12. DanJS

when h = 9

13. DanJS

$V = \frac{ 3 }{ 25 }\pi*h^3$

14. DanJS

chain rule $\frac{ dV }{ dt }=[\frac{ 3 }{ 25 }\pi]*3h^2*\frac{ dh }{ dt }$

15. DanJS

you are given h and dh/dt, find dV/dt