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Homework Help: A Cubic Volume Problem

  1. Oct 5, 2016 #1
    • Member warned that the homework template is required
    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. jcsd
  3. Oct 5, 2016 #2


    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##.
  4. Oct 5, 2016 #3


    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    That doesn't sound right. We are given that ##V=825##, not ##V=825\pi##.
  5. Oct 5, 2016 #4
    Sorry, I forgot to add 825pi as the volume.
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