Question

The height of a rectangular prism is half its width The width of the prism is 1/3 of its length If the width of the prism is 3 centimeters, what is the volume?

Answer 1

40.5 centimeters.

Explanation:

Given:

The width of the prism is 3 centimeters.

The width of the prism is 1/3 of its length.

The height of a rectangular prism is half its width.

To find:

Volume of a rectangular prism = ?

Solution:

Width of the prism = 3 cm

As given, height of a rectangular prism is half its width.

height of a rectangular prism =
`(1)/(2) *3=(3)/(2) \ cm`

Similarly, as given, the width of the prism is 1/3 of its length.

Width of the prism =
`(1)/(3)\ of\ length`

`3=(1)/(3)* length`

By multiplying both sides by 3

`3*3=(1)/(3) *3\ length\\9= length\\`

Thus, length of prism = 9 cm

Now, as we know:

`Volume\ of\ rectangular\ prism=length* breadth* height`

`=9*3*(3)/(2) \\\\ =(81)/(2) \\ \\ =40.5\ cm`

Therefore, the volume of a rectangular prism is 40.5 centimeters.