Question

A caterer wants to have cylinder water glasses completely full, including three ice cubes. The water is going to be poured first and the ice cubes added once the glasses are on the table. The diameter of the water glass is 3 in and the height is 6 in. The ice cubes are perfect cubes with side lengths of 1.5 in. What volume of water needs to be added so that adding the ice cubes completely fills each glass?

Answer 1

First we need to determine the volume of the glass

The glass is a cylinder

V = pi r^2 h

We have the diameter so we need to find the radius

r = d/2 = 3/2 = 1.5

V = pi ( 1.5)^2 ( 6)

V = 13.5 pi in ^3

We are putting in 3 ice cubes

The volume of one ice cube is

V = s^3

V = 1.5 ^3

V =3.375

Multiply by 3

3 * 3.375 = 10.125 in^3

We need to subtract the ice cube volume from the total volume

13.5 pi - 10.125

We need (13.5 pi - 10.126) in^3 of water