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

cylindrical vessel holds the most root beer

Explanation:

Given:

For Euclid'r root bee mug (cylinder):

Height of mug (h)= 8 inches

Radius of mug (r)= 3 inches

For Aristotle’s root beer glass (cone):

Height of mug (H)= 18 inches

Diameter of mug (D)= 4 inches

To find: vessel which holds the most root beer

Solution:

Volume of cylinder =
`\pi r^2 h=\pi(3)^2 (8)=72 \pi` cubic inches

As diameter of cone is 4 inches,

Radius (R) = diameter/2 = 4/2 = 2 inches

Volume of cone =
`(1)/(3)\pi R^2H=(1)/(3)\pi(2)^2(18)=24 \pi` cubic inches

So, volume of cylinder > volume of cone

Hence,

cylindrical vessel holds the most root beer