SOLUTION: Water is poured into a conical container with a diameter of 20 cm and a height of 38 cm. If the volume of a cone is one-third the volume of a cylinder, write an equation for the vo

Question 92944: Water is poured into a conical container with a diameter of 20 cm and a height of 38 cm. If the volume of a cone is one-third the volume of a cylinder, write an equation for the volume of water as a function of the height of the water in the container.
Answer by kev82(151) (Show Source): You can put this solution on YOUR website!
Hi,

First things first, you need to know the formula for the volume of a cone is

Which, as the question says is a third the volume of a cylinder.

We need to know the volume when the water is at height h. So this means for a given h, we need to figure out r.

By the definition of a cone, for any point on the cone's surface (apart from the tip) the ratio of r and h is constant. To understand that, think of a cone as a line in the x-y plane rotated about the x axis. The ratio of r and h is simply the gradient of that line.

So

. Substituting this in to the formula for the volume of a cone gives:

Kev
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