Question

Easy please help!! Popcorn at a concession stand comes in two different-sized containers. The dimensions of the small container with a diameter of 4 in. are shown below.

A popcorn container shaped like a cylinder is shown. A dashed line across the top of the container is labeled four inches. The height of the container is labeled four and five tenths inches.


The large container of popcorn has the same height as the small container, but its diameter is 1.5 times greater. How do the volumes of the two containers of popcorn compare? Use 3.14 for π.


Select the answers from the drop-down lists to correctly complete each sentence.


The volume of the large container of popcorn is _______ in.^3

OPTIONS FOR BLANK :

A) 56.52

B) 84.78

C)127.17

D) 169.56


This is ______ times the volume of the small container.

OPTIONS FOR THIS BLANK :

A) 2.88

B) 2.25

C) 1.8

D) 1.5

Answer 1

• 127.17 cubic inches
• 2.25 times

Explanation:

You want to know the volume of a cylindrical container 6 inches in diameter and 4.5 inches high, and you want to know how many times larger this volume is than if the diameter were 4 inches.

Volume

The volume of a cylinder is given by the formula ...

V = πr²h

where r is half the diameter, and h is the height.

The volume of your large popcorn container is ...

V = 3.14·(3 in)²·(4.5 in) = 127.17 in³

The volume of the large container is 127.17 in³.

Ratio

For a given height, the volume ratio is the square of the ratio of diameters. That ratio is given as 3/2, so the volume ratio is ...

(3/2)² = 9/4 = 2.25

The large container is 2.25 times the volume of the small container.