Question

A rectangular prism has a length of 312 inches, a width of 5 inches, and a height of 112 inches. What is the volume of the prism? Enter your answer in the box as a simplified mixed number or a decimal.

Answer 1

Answer:
`26(1)/(4)\text{ inches}^3`

Explanation:

Given : In a rectangular prism , length =
`3(1)/(2)\text{ inches}`

`=(3(2)+1)/(2)=(7)/(2)\text{ inches}`

width = 5 inches

height=
`1(1)/(2)\text{ inches}=(3)/(2)\text{ inches}`

Now, the volume of the prism will be :-

`V= l* w* h\\\\=(7)/(2)*5*(3)/(2 )\text{ inches}^3\\\\=(105)/(4)\text{ inches}^3\\\\=26(1)/(4)\text{ inches}^3`

Hence, the volume of the prism
`=26(1)/(4)\text{ inches}^3`

Answer 2

The volume of the prism in the decimal form is 26.25 inches³ and
`26 (1)/(4)\ inches^(3)`

Explanation:

Formula

Volume of a rectangular prism = Length × Breadth × Height

As given

A rectangular prism has a length of
`3 (1)/(2)`inches, a width of 5 inches, and a height of
`1 (1)/(2)` inches.

i.e

A rectangular prism has a length of
`(7)/(2)`inches, a width of 5 inches, and a height of
`(3)/(2)` inches.

`Volume\ of\ a\ rectangular\ prism = (7)/(2)* 5* (3)/(2)`

`Volume\ of\ a\ rectangular\ prism = (7* 5** 3)/(2* 2)`

`Volume\ of\ a\ rectangular\ prism = (105)/(4)`

In mixed number

`Volume\ of\ a\ rectangular\ prism =26 (1)/(4)\ inches^(3)`

In decimal form

`Volume\ of\ a\ rectangular\ prism = 26.25\ inches^(3)`

Therefore the volume of the prism in the decimal form is 26.25 inches³ and
`26 (1)/(4)\ inches^(3)`