Question

A new company wants to mail out samples of its hair products. The company has a sample box that is a rectangular prism with a rectangular base with an area of 23 1/3 in². The height of the prism is 1 1/4 in. Determine the volume of the sample box.

Answer 1

The volume of the rectangular prism is
`\tfrac{175}{6} in^(3)`.

Explanation:

Here, box is in the shape of rectangular prism means cuboid shape.

Given:

Rectangular prism base area is
`23\tfrac{1}{3}` in².

Height of the prism is
`1\tfrac{1}{4}` in.

Calculation:

Volume of the rectangular prism is nothing but the volume of cuboid.

Volume of the cuboid is expressed as follow:

V=lbh …… (1)

Base are of the rectangular prism is expressed as follows:

A=lb …… (2)

Substitute the equation (2) in (1). We get the expression for volume as follows:

V=Ah

Substitute
`23\tfrac{1}{3}` in² for A and
`1\tfrac{1}{4}` in for h in above equation as follows:

`V=23\tfrac{1}{3}* 1\tfrac{1}{4}`

`V=\tfrac{70}{3}* \tfrac{5}{4}`

`V=\tfrac{175}{6} in^(3)`

Thus, the volume of the rectangular prism is
`\tfrac{175}{6} in^(3)`.