Question

i need help with related rates please
my problem is this

Sand is falling off a conveyor belt onto a conical pile at the rate of 10 cubic ft per minute. the diameter of the base of the cone is approximately twice the altitude. At what rate is the height of the pile changing when it is 5 ft. high?

An explanation and the steps would be extremely helpful.

Answer 1

" at the rate of 10 cubic ft per minute."

we need formula for volume of cone
it is
V= 1/3 Pi r^2 h

"the diameter of the base of the cone is approximately twice the altitude."
which say
r=h

we may write
V= 1/3 Pi h^3

now let's differentiate

dv/dh= 1/3 Pi 3h^2= Pi h^2

dv= pi h^2 dh

Answer 2

"10 cubic ft per minute."
dv=10

"At what rate is the height of the pile changing when it is 5 ft. high"
h=5
10= pi 5^2 dh

10
---- = dh
pi 25

Answer 3

thank you so much