Question

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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 base area of 17 1/4 ft² and a height of 4 ft. find its volume. (b) the other crate has a volume of 28 4/5 ft³, a length of 6 ft, and a height of 1 1/5 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: Solve for volume in part (a)

Given $B = 17\frac{1}{4}=\frac{17\times4 + 1}{4}=\frac{69}{4}$ square - feet and $h = 4$ feet. Then $V=B\times h=\frac{69}{4}\times4 = 69$ cubic - feet.

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 $V = 28\frac{4}{5}=\frac{28\times5+4}{5}=\frac{144}{5}$ cubic - feet, $l = 6$ feet, and $h = 1\frac{1}{5}=\frac{1\times5 + 1}{5}=\frac{6}{5}$ feet.

Step4: Substitute values into the formula and solve for $w$

Substitute into $V=l\times w\times h$: $\frac{144}{5}=6\times w\times\frac{6}{5}$. First, simplify the right - hand side: $6\times\frac{6}{5}\times w=\frac{36}{5}w$. Then solve for $w$ by cross - multiplying: $144 = 36w$. So, $w = 4$ feet.

Answer:

(a) $69$ ft³
(b) $4$ ft