Question

company sells two storage containers with different dimensions. each container is shaped like a rectangular prism. use the given information to answer each part below. (a) one container has a base area of 15 ft² and a height of 1 1/2 ft. find its volume. (b) the other container has a volume of 33 ft³, a length of 3 ft, and a height of 5 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: Calculate volume for part (a)

Given $B = 15$ ft² and $h=1\frac{1}{2}=\frac{3}{2}$ ft. Then $V=B\times h = 15\times\frac{3}{2}=\frac{45}{2}=22.5$ ft³.

Step3: Recall volume formula for rectangular - prism for part (b)

The volume formula for a rectangular prism is $V = l\times w\times h$. We know $V = 33$ ft³, $l = 3$ ft, and $h = 5$ ft. We need to find $w$.

Step4: Rearrange the formula to solve for $w$

From $V=l\times w\times h$, we can get $w=\frac{V}{l\times h}$.

Step5: Substitute values to find $w$

Substitute $V = 33$ ft³, $l = 3$ ft, and $h = 5$ ft into the formula: $w=\frac{33}{3\times5}=\frac{33}{15}=\frac{11}{5}=2.2$ ft.

Answer:

(a) Volume = 22.5 ft³
(b) Width = 2.2 ft