Question

mr. carlo is building a storage box in his workshop. the space where he plans to put the box is 5 feet long and 2 feet wide. he wants the volume of the box to be at least 36 cubic feet but no more than 56 cubic feet. how tall should mr. carlo make the box? explain. show your work. you can start by finding the number of cubic feet in 1 layer.

Explanation:

Step1: Recall volume formula

The volume formula for a rectangular - prism (the storage box) is $V = l\times w\times h$, where $l$ is length, $w$ is width and $h$ is height. We know that $V\geq36$ and $V\leq56$, $l = 5$ feet and $w = 2$ feet.

Step2: Substitute values into formula

Substitute $l = 5$ and $w = 2$ into the volume formula $V=l\times w\times h$, we get $V = 5\times2\times h=10h$.

Step3: Solve for height range

Since $36\leq V\leq56$, then $36\leq10h\leq56$. Divide each part of the compound - inequality by 10. For the left - hand side, $\frac{36}{10}\leq h$, which simplifies to $h\geq3.6$. For the right - hand side, $h\leq\frac{56}{10}=5.6$.

Answer:

The height $h$ of the box should satisfy $3.6\leq h\leq5.6$ feet.