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

Answer:

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

Step-by-step 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:

$V=23\tfrac{1}{3}\times 1\tfrac{1}{4}$

$V=\tfrac{70}{3}\times \tfrac{5}{4}$

$V=\tfrac{175}{6} in^{3}$

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