Taylor has a punch bowl shaped like a cylinder, with a diameter of 22 inches and a height of 20 inches, she pours 8.25 gallons of punch into the bowl. (note 1 gallon = 231 cubic inches)

Question

How far from the top of the punch bowl is the top of the punch?

Answer 1

Okay, so the key to this is to compare the two. You know that the cylinder has a bottom area of 121π. As the punch is poured in, it takes the shape of the cylinder and fills up, so the punch effectively forms a smaller cylinder within the bowl, with the small base area.

Since the Volume of the punch = 121π * (height of the punch). Since the volume of punch = 8.25 * 231 = 1905.75. So 1905.75 = 121π * h.

So, h = 5.01in. Since the punch bowls height is 20in, the distance to the top is 14.99in