You are choosing between two mugs. One has a base that is 5.5 inches in diameter and a height of 3 inches. The other has a base of 4.5 inches in diameter and a height of 4 inches. You want the one that holds the most! Which should you choose. Include the formulas and correct units of measure that you found when solving the problem.

We should choose mug 1 having volume of  71.24 inch³ ,with diameter 5.5 inches and height 3 inches holds the most !

Step-by-step explanation:

We have 2 mugs, One has a base that is 5.5 inches in diameter and a height of 3 inches. The other has a base of 4.5 inches in diameter and a height of 4 inches. Basically, mugs are cylinders so we will consider 2 cylinders .

To find which one holds the most we are supposed to find volume of both ,the one with maximum volume holds the most.

Part 1:

volume of cylinder 1 ()= πr₁²h₁ ,

r₁ = radius of cylinder ⇒

h₁ = height of cylinder ⇒  3 inches

∴ = πr₁²h₁

⇒ 3.14×( 2.75 )²×3 ⇒ 71.24 inch³

Part 2:

volume of cylinder 2 ( )= πr₂²h₂

r₂ = radius of cylinder ⇒

h₂ = height of cylinder ⇒  4 inches

∴ = πr₂²h₂

⇒ 3.14×( 2.25 )²×4 ⇒ 63.59 inch³

∵ ( 71.24 inch³ ) > ( 63.59 inch³ ), mug 1 with diameter 5.5 inches and height 3 inches holds the most.