Question

skylar models the volume of a popcorn box as a right rectangular prism and the box can hold 69 cubic inches of popcorn when it is full. its width is 3 in and its height is $5\frac{3}{4}$ in. find the length of the popcorn box in inches. round your answer to the nearest tenth if necessary.

Explanation:

Step1: Convert the mixed number to an improper fraction

The height \(h = 5\frac{3}{4}=\frac{5\times4 + 3}{4}=\frac{23}{4}\) inches.
The formula for the volume \(V\) of a right - rectangular prism is \(V=l\times w\times h\), where \(l\) is the length, \(w\) is the width, and \(h\) is the height. We know that \(V = 69\) cubic inches, \(w = 3\) inches, and \(h=\frac{23}{4}\) inches.

Step2: Substitute the values into the volume formula and solve for \(l\)

Substitute into \(V=l\times w\times h\):

$$69=l\times3\times\frac{23}{4}$$

First, simplify the right - hand side: \(3\times\frac{23}{4}=\frac{69}{4}\). So the equation becomes \(69 = l\times\frac{69}{4}\).
To solve for \(l\), use the formula \(l=\frac{V}{w\times h}\). Multiply both sides of the equation \(69 = l\times\frac{69}{4}\) by \(\frac{4}{69}\).

$$l=\frac{69\times4}{69}$$

Cancel out the common factor of \(69\).

Answer:

\(l = 4\) inches.