Related Rates Sand Pile Problem

[Mr Davis 97]

Homework Statement

A machine starts dumping sand at the rate of 20 m3/min, forming a pile in the shape of a cone. The height of the pile is always twice the length of the base diameter. After 5 minutes, how fast is the height increasing? After 5 minutes, how fast is the area of the base increasing?

Homework Equations

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

The Attempt at a Solution

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For the first question,
$h = 4r$
$\displaystyle V(t) = 20t = \frac{1}{3}\pi r^2 h = \frac{\pi}{48}h^3$
From this equation I get
$\displaystyle h = (\frac{960}{\pi}t)^{\frac{1}{3}}$
then
$\frac{dh}{dt} = \frac{320}{\pi ((\frac{960}{\pi})t)^{\frac{2}{3}}}$
When 5 is substituted for t, I get 0.77 m^3/min. Is this correct?

Also, I am not sure how to approach the second problem. I know that the area of the base is $\pi r^2$, but I am not sure how to proceed...

 

[Thewindyfan]

Use the fact that height is equal to twice the diameter of the base at all times.

 

[Mr Davis 97]

Use the fact that height is equal to twice the diameter of the base at all times.

I did that for the first problem. I don't see how it will work for the second problem though.

 

[Thewindyfan]

I did that for the first problem. I don't see how it will work for the second problem though.

EDIT: ah never mind, fairly straightforward problem. Haven't seen one like this in awhile though.

Method 1: If you're know what dH/dt is, try applying that to see what the radius would be.

EDIT: you did the first part right.
Suggested Hint: Try rewriting the area equation.

...and check your units to part 1.