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 1/4 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: Calculate volume for part (a)

Given $l = 3$ ft, $w=2\frac{1}{4}=\frac{9}{4}$ ft and $h = 4$ ft. Then $V=3\times\frac{9}{4}\times4$. First, $3\times\frac{9}{4}=\frac{27}{4}$, and $\frac{27}{4}\times4 = 27$ $ft^{3}$.

Step3: Recall height - volume - base - area relationship for part (b)

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

Step4: Calculate height for part (b)

Given $V = 33$ $ft^{3}$ and $B = 16\frac{1}{2}=\frac{33}{2}$ $ft^{2}$. Then $h=\frac{33}{\frac{33}{2}}$. Using the rule of dividing by a fraction ($a\div\frac{b}{c}=a\times\frac{c}{b}$), we have $h = 33\times\frac{2}{33}=2$ ft.

Answer:

(a) $27$
(b) $2$