We should choose mug 1 having volume of 71.24 inch³ ,with diameter 5.5 inches and height 3 inches holds the most !
<u>Step-by-step explanation:</u>
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.
<u>Part 1: </u>
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
<u>Part 2:</u>
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.