# A Cubic Volume Problem

1. Oct 5, 2016

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The question reads, "Find the dimensions of a cylindrical tennis ball container which has the volume of V(x)=8πx3+17πx2+10πx+π such that the volume is exactly 825π cm3. Hint: V = πr2h."

To start off, I set V(x)=825π and moved it to the right side, giving

0 = 8πx3+17πx2+10πx-824π.

Factoring pi, we get 0 = π(x-4)(8x2+49x+206),

Since we can't factor the second bracket, here's where I get confused. My inference is that the radius is 4 cm, and the height is muzzled in that unfactorable bracket. However, having the equation for volume (V = πr2h), I get h = 825/16π.

Can someone verify this for me, please?

Last edited: Oct 5, 2016
2. Oct 5, 2016

### Staff: Mentor

Looks fine to me, but you should write that number as 825/(16π). Many people would interpret what you wrote as $\frac{825}{16}\pi$.

3. Oct 5, 2016

### andrewkirk

That doesn't sound right. We are given that $V=825$, not $V=825\pi$.

4. Oct 5, 2016

Sorry, I forgot to add 825pi as the volume.