A cone-shaped container is oriented with its circular base on the top and its apex at the bottom. It has a radius of 18 inches and a height of 6 inches. The cone starts filling up with water. What fraction of the volume of the cone is filled when the water reaches a height of 2 inches?

GAMEMASTERX40 Apr 7, 2020

#1**+2 **

The water will reach a height of 2 inches creating a similar cone. Since the ratio of the height of the smaller to the larger cone is 2:6 or 1:3, that means that the radius of the cones are in a ratio of 1:3 meaing the smaller cone has a radius of 6. Knowing this, the volume of a cone is 1/3Bh, where B is area of base and h is the height so we get 1/3*36pi*2= **24 pi**.

Hope it helps!

HELPMEEEEEEEEEEEEE Apr 7, 2020

#2**+1 **

The fast way to do it is to realize that the ratio of corresponding side lengths is 1 to 3. The ratio of volumes of similar shapes is ration of sides cubed. So the ratio of the volumes would be 1^3 to 3^3 or 1 to 27.

So if the large cone has a volume of 648pi, then **648pi/27= 24pi**. This is a neat trick to know and works with area as well.

Hope it helps!

HELPMEEEEEEEEEEEEE Apr 7, 2020