Question

A movie theater offers two containers which container is the better value use 3.14 as an approximation for pi 

Answer 1

cylinder

Explanation:

You want to know which of two popcorn containers is a better value:

• cone: diameter 12 cm, height 19 cm, cost $6.75
• cylinder: diameter 8 cm, height 15 cm, cost $6.25

Volume

The volume formulas for the two shapes are ...

V = 1/3πr²h . . . . . cone

V = r²h . . . . . . . . . cylinder

Ratio

For r = d/2, the ratio of these two volumes is ...

`(V_(con))/(V_(cyl))=((1)/(3)\pi\left((d_(con))/(2)\right)^2h_(con))/(\pi\left((d_(cyl))/(2)\right)^2h_(cyl))=(d_(con)^2\cdot h_(con))/(3\cdot d_(cyl)^2\cdot h_(cyl))=(12^2\cdot19)/(3\cdot 8^2\cdot 15)=(2736)/(2880)=0.95`

The cone has less volume and costs more, so the cylindrical container is the better value.