- #1

Burjam

- 52

- 1

## Homework Statement

Grit, which is spread on roads in winter, is stored in mounds which are the shape of a cone. As grit is added to the top of a mound at 2 cubic meters per minute, the angle between the slant side of the cone and the vertical remains 45º. How fast is the height of the mound increasing when it is half a meter high?

## Homework Equations

V=πr

^{2}/3

## The Attempt at a Solution

So I need to solve for dh/dt. I know dV/dt=2 and I know the height, but not the radius. So I draw a right triangle. Since the angle is 45º, r=h. So r=0.5. Now time to take d/dt of each side.

dV/dt=d/dt[πr

^{2}/3]

2=1/3πr

^{2}*dh/dt

I treated r as a constant and h as a function of time here. I applied the product rule and the chain rule.

dh/dt=6/πr

^{2}

Substitue 0.5 for r and I get

dh/dt=24/π

The correct answer is 8/π. Where did I go wrong?