Question

a company sells two storage containers with different dimensions. each container is shaped like a rectangular prism. use the given information to answer each below. (a) one container has a base area of 24 ft² and a height of 1 1/5 ft. find its volume. (b) the other container has a volume of 33 ft³, a length of 3 ft, and a height of 4 ft. find its width.

Explanation:

Step1: Recall volume formula for rectangular prism

The volume formula for a rectangular prism is $V = B\times h$, where $B$ is the base - area and $h$ is the height.

Step2: Convert the mixed - number to an improper fraction

$1\frac{1}{5}=\frac{1\times5 + 1}{5}=\frac{6}{5}$

Step3: Calculate the volume of the first container

$V=24\times\frac{6}{5}=\frac{24\times6}{5}=\frac{144}{5} = 28.8$ $ft^{3}$

For part (b):

Step1: Recall the volume formula for a rectangular prism

The volume formula for a rectangular prism is $V=l\times w\times h$, where $V$ is volume, $l$ is length, $w$ is width and $h$ is height. We can solve for $w$: $w=\frac{V}{l\times h}$

Step2: Substitute the given values

Given $V = 33$ $ft^{3}$, $l = 3$ $ft$ and $h = 4$ $ft$. Then $w=\frac{33}{3\times4}=\frac{33}{12}=\frac{11}{4}=2.75$ $ft$

Answer:

(a) $28.8$ $ft^{3}$
(b) $2.75$ $ft$