Question

Which has a greater volume; two regular cans of soup, each with a diameter of 8 cm and a height of 10 cm or one family size can of soup, which has a diameter of 10 cm and a heigh if 12 can? Explain and give your calculations.

Answer 1

The two regular cans of soup has a greater volume than the family size can of soup

Explanation:

step 1

Find the volume of two regular cans of soup, each with a diameter of 8 cm and a height of 10 cm

The volume is equal to

`V=2[\pi r^(2) h]`

we have

`r=8/2=4\ cm` ----> the radius is half the diameter

`h=10\ cm`

substitute

`V=2[\pi (4)^(2) (10)]`

`V=320\pi\ cm^(3)`

step 2

Find the volume of one family can of soup, with a diameter of 10 cm and a height of 12 cm

The volume is equal to

`V=\pi r^(2) h`

we have

`r=10/2=5\ cm` ----> the radius is half the diameter

`h=12\ cm`

substitute

`V=\pi (5)^(2) (12)`

`V=300\pi\ cm^(3)`

therefore

Compare the volumes

`320\pi\ cm^(3) > 300\pi\ cm^(3)`

The two regular cans of soup has a greater volume than the family size can of soup