Question

A juice stand sells smoothies in cone-shaped cups that are 8 in. tall. The regular size has a 4 in. diameter. The jumbo size has an 8 in. diameter. Find the volume of the regular size and the jumbo size to the nearest tenth of a cubic inch.

Answer 1

All cone-shaped cups have the same height in 8 inches. They just differ in their diameters. To solve for the volume of the regular and jumbo sizes, let's use the formula for the volume of cone

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

r is just the half of the diameter, h is the height which is equal to 8

Regular size:
V = (1/3)*pi*((4/2)^2)*8
V = 33.5 cube inches

Jumbo size:
V = (1/3)*pi*((8/2)^2)*8
V = 134.0 cube inches