Question

Sand is being poured on the ground at the rate of 25m^3/min forming a conical pile whose altitude is the same as the radius of the base. How fast is the altitude increasing when the diameter of the base is 12m?

Answer 1

set up your equation

Answer 2

V= 1/3pi(r)^2h

Answer 3

and what is the question?

Answer 4

I'm not sure how to find the rate of the altitude?

Answer 5

25m^3/min forming a conical pile whose altitude is the same as the radius of the base
ow fast is the altitude increasing when the diameter of the base is 12m?

Answer 6

\(V'(t) = 25 \) and you need \(r(t) \) = \(h(t)\)

Answer 7

\(r(t) = \frac{d}{2} = 6\)

Answer 8

d=12

Answer 9

ye, but your equation for volume uses radius and not diameter

Answer 10

radius and the height are both 6m

Answer 11

ye

Answer 12

do I sub the 6 into the equation for both radius and height?

Answer 13

so you're solving for \(\huge \frac{dh}{dt}\)

Answer 14

but you need \(\large \frac{dV}{dt} =\)

Answer 15

25

Answer 16

equation

Answer 17

then put the value

Answer 18

how about this, try to draw what is going on

Answer 19

v=1/3pi(6^2(h))
dv/dt=12pi[dh/dt]

Answer 20

I think it will help you if you can visually interpret it

Answer 21

the reason why I am asking is because you're given a diameter, which tells you the area of the base

Answer 22

Im not sure how to draw it, but I could try...