Question

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.

Answer 1

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 ($V_{1}$)= πr₁²h₁ ,

r₁ = radius of cylinder ⇒ $\frac{\text {diameter}}{2}=\frac{5.5}{2}=2.75 \text { inches }$

h₁ = height of cylinder ⇒  3 inches

∴ $V_{1}$ = πr₁²h₁

⇒ 3.14×( 2.75 )²×3 ⇒ 71.24 inch³

Part 2:

volume of cylinder 2 ( $V_{2}$ )= πr₂²h₂

r₂ = radius of cylinder ⇒ $\frac{\text {diameter}}{2}=\frac{4.5}{2}=2.25 \text { inches }$

h₂ = height of cylinder ⇒  4 inches

∴ $V_{2}$ = πr₂²h₂

⇒ 3.14×( 2.25 )²×4 ⇒ 63.59 inch³

∵ $V_{1}$ ( 71.24 inch³ ) > $V_{2}$ ( 63.59 inch³ ), mug 1 with diameter 5.5 inches and height 3 inches holds the most.