Question

Gravel is being dumped from a conveyor belt at a rate of 20 cubic feet per minute. It forms a pile in the shape of a right circular cone whose base diameter and height are always equal. How fast is the height of the pile increasing when the pile is 21 feet high?

Recall that the volume of a right circular cone with height h and radius of the base r is given by
V=1/3πr^(2)h

Answer 1

@Chlorophyll ok so first start by deriving the function (2 pi h r)/3

Answer 2

wow that's tough

Answer 3

then if im not missing anything if you plugged in (2 pi (21) (20))/3
but i feel as if thats way to easy to be right

Answer 4

volume is 1/3 *pi *r2*h

Answer 5

and ya it is tough thats why im on here

Answer 6

correct

Answer 7

Since the "diameter and height are always equal "
-> 2r = h
=> r = h/2
Now plug r into the volume v. We utilize the relationship to obtain only 1 variable h:
V= 1/3π r² h

Answer 8

@NickR Questions?

Answer 9

V=1/12 *pi *h3

Answer 10

differentiate with respect to time

Answer 11

u know dv/dt=20 cubic/min

Answer 12

plug in to the equation dV/dt=1/4* pi *h2*dh/dt

Answer 13

h=21 dv/dt=20

Answer 14

um so V= 1/3π (h/2)² h

Answer 15

dh/dt=0.057

Answer 16

Yup, convert the equation into 1indepent variable prior to taking derivative!

Answer 17

plz give me medal

Answer 18

thanks

Answer 19

i will tell this to my mom that i got a medal

Answer 20

(pi h^2)/4
(pi 21^2)/4

Answer 21

@Fazeelayaz you're truly deserved it :)

Answer 22

@NickR Following @Fazeelayaz post staring from :
V = ( π/12 ) h³

Answer 23

*starting from:

Answer 24

20=1/4* pi *21^2*.057

Answer 25

=> h' = 80/ 21² π

Answer 26

is that the answer?

Answer 27

Yes, h' = .057 ft/min

Answer 28

oh ok didnt know pi was in denominator

Answer 29

Feel free to ask questions :)

Answer 30

ok sorry to keep bothering you but got one more question if you could look at it and this time i actually know how to do it.

Answer 31

Okie, open new post :)