Question

a pet shop sells two crates with different dimensions. each crate is shaped like a rectangular prism. use the given information to answer each part below. (a) one crate has a length of 3 ft, a width of 2 3/4 ft, and a height of 4 ft. find its volume. (b) the other crate has a volume of 33 ft³ and a base area of 16 1/2 ft². find its height.

Explanation:

Step1: Recall volume formula for rectangular prism

The volume formula for a rectangular prism is $V = l\times w\times h$, where $l$ is length, $w$ is width and $h$ is height.

Step2: Convert mixed - number to improper fraction

The width $w = 2\frac{3}{4}=\frac{2\times4 + 3}{4}=\frac{11}{4}$ ft, $l = 3$ ft and $h = 4$ ft.

Step3: Calculate volume for part (a)

$V=3\times\frac{11}{4}\times4$
$V = 3\times11=33$ ft³.

Step4: Recall relationship between volume, base - area and height for rectangular prism

The volume formula can also be written as $V=B\times h$, where $B$ is the base - area and $h$ is the height. So, $h=\frac{V}{B}$.

Step5: Convert mixed - number to improper fraction for part (b)

The base - area $B = 16\frac{1}{2}=\frac{16\times2+1}{2}=\frac{33}{2}$ ft² and $V = 33$ ft³.

Step6: Calculate height for part (b)

$h=\frac{33}{\frac{33}{2}}=33\times\frac{2}{33}=2$ ft.

Answer:

(a) $33$ ft³
(b) $2$ ft