Expert: Steve Holleran - 5/29/2007

Question
A circular can has a height equal to its diameter and holds one liter



a) What is its height?

b) If the can holds 8 liters, what is its height?

c) If the can holds V liters, what is its height?


Answer
Hi Levi,

First, let's call the diameter d and the radius r and the height h.

So then, d = 2r and h = 2r.

The volume formula for a cylinder is V = pi * r^2 * h

So, in the first case, we also need to note that 1 liter = 1000 ml = 1000 cm^2 to get to a volume unit and away from a capacity unit.  We then have :

  1000 = pi * r^2 * (2r)

  1000 = pi * 2r^3

solving for r, we get r^3 = 1000 / 2pi = 500/pi

and       r = cu rt(500/pi) = 5.42,

 so here h = 2(5.42) = 10.84.

Parts B and C are similar:

B)  8000 = pi * 2r^3  so r = cu rt(8000/2pi) = 10.84

   so h = 21.68

C)   V = pi * 2r^3  so r = cu rt(V / 2pi) and then in

   general, h = 2 * cu rt(V / 2pi)

I hope this helps

Steve Holleran