Question

A cereal box has the following dimensions: length = 19 cm, width = 3 cm, height = 27 cm. If 2 cubic centimeters of space in the box holds 30 pieces of cereal, how many pieces of cereal would you expect in the box (assuming there is no header space at the top and there is no settling at the bottom). When you write your answer, do not put any commas and do not use any decimals.

Answer 1

There are 23085 pieces of cereal in the box.

Explanation:

Given dimension of the box;

Length = 19 cm

Width = 3 cm

Height = 27 cm

For finding the capacity of the box we should find out the volume of the box.

Volume of box =
`length* width* height`

Volume of box =
`19*3*27=1539\ cm^3`

Now, according to question;

`2\ cm^3` of space in the box holds 30 pieces of cereal.

To find out the number of cereal in the box we use the unitary method.

∵
`2\ cm^3` of space in the box holds 30 pieces

∴
`1\ cm^3` of space in the box =
`(30)/(2)`

∴
`1539\ cm^3` of space in the box =
`(30)/(2)*1539=15*1539= 23085`.

Hence there are 23085 pieces of cereal in the box.