Question

A water cup in the shape of a cone has a height of 4 inches and a maximum diameter of 3 inches. What is the volume of the water cup, to the nearest tenth of a cubic inch, when the cup is filled to half its height

Answer 1

1.2 in3

Explanation:

The volume of a cone is given by the following formula:

Volume = (1/3) * pi * r^2 * h

Where r is the base radius and h is the height.

So, if the full cone height is 4 inches and the diameter is 3 inches (that is, the radius is 3/2 = 1.5 inches), we have that half of the cone's height is 2 inches, and the diameter will be 1.5 inches (so the radius is 0.75 inches). Then, the volume of half the cup is:

Volume = (1/3) * pi * 0.75^2 * 2 = 1.1781 in3

Rounding to nearest tenth, the volume is 1.2 in3