Respuesta :
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 ([tex]V_{1}[/tex])= πr₁²h₁ ,
r₁ = radius of cylinder ⇒ [tex]\frac{\text {diameter}}{2}=\frac{5.5}{2}=2.75 \text { inches }[/tex]
h₁ = height of cylinder ⇒ 3 inches
∴ [tex]V_{1}[/tex] = πr₁²h₁
⇒ 3.14×( 2.75 )²×3 ⇒ 71.24 inch³
Part 2:
volume of cylinder 2 ( [tex]V_{2}[/tex] )= πr₂²h₂
r₂ = radius of cylinder ⇒ [tex]\frac{\text {diameter}}{2}=\frac{4.5}{2}=2.25 \text { inches }[/tex]
h₂ = height of cylinder ⇒ 4 inches
∴ [tex]V_{2}[/tex] = πr₂²h₂
⇒ 3.14×( 2.25 )²×4 ⇒ 63.59 inch³
∵ [tex]V_{1}[/tex] ( 71.24 inch³ ) > [tex]V_{2}[/tex] ( 63.59 inch³ ), mug 1 with diameter 5.5 inches and height 3 inches holds the most.
