Question

Euclid’s root beer mug is shaped basically like a cylinder that is eight inches tall with a radius of three inches. Aristotle’s root beer glass is shaped basically like a cone that is 18 inches tall with a diameter of four inches. Which vessel holds the most root beer?

Answer 1

Answer:

The root beer mug

Step-by-step explanation:

To known what vessels holds more root beer, we must find the volume (this is the holding capacity) of the two vessels. From the description given, the mug is a cylinder while the glass is a cone.

The volume V of a cylinder whose height is h and radius r may be found as

V = πr²h

The volume V of a cone with similar features

V  = 1/3πr²h

Hence the volume of the mug shaped basically like a cylinder that is eight inches tall with a radius of three inches

=  π * 3² * 8

= 72π Inches³

Given that the cone shaped bottle has a diameter of four inches, the radius r = 4/2

= 2 inches

Hence the volume of the bottle

= 1/3 * π * 2² * 18

= 24π Inches³

Based on comparison, the mug holds more root beer