Question

Samir 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
4, start fraction, 3, divided by, 4, end fraction
4 3/4
​
in and its height is
7, one quarter
7 1/4
​
in. Find the length of the popcorn box in inches. Round your answer to the nearest tenth if necessary.

Answer 1

To find the length of the popcorn box modeled as a right rectangular prism, we can use the formula for the volume of a rectangular prism:

\[
\text{Volume} = \text{Length} \times \text{Width} \times \text{Height}
\]

We know the volume is 69 cubic inches, the width is \(4 \frac{3}{4}\) inches, and the height is \(7 \frac{1}{4}\) inches. First, we need to convert the mixed numbers to improper fractions.

**Converting \(4 \frac{3}{4}\):**

\[
4 \frac{3}{4} = 4 + \frac{3}{4} = \frac{16}{4} + \frac{3}{4} = \frac{19}{4}
\]

**Converting \(7 \frac{1}{4}\):**

\[
7 \frac{1}{4} = 7 + \frac{1}{4} = \frac{28}{4} + \frac{1}{4} = \frac{29}{4}
\]

Now we can substitute these values into the volume formula:

\[
69 = \text{Length} \times \frac{19}{4} \times \frac{29}{4}
\]

Now we calculate \(\frac{19}{4} \times \frac{29}{4}\):

\[
\frac{19 \times 29}{4 \times 4} = \frac{551}{16}
\]

So, we have:

\[
69 = \text{Length} \times \frac{551}{16}
\]

Next, we isolate the Length:

\[
\text{Length} = 69 \div \frac{551}{16} = 69 \times \frac{16}{551} = \frac{69 \times 16}{551}
\]

Calculating \(69 \times 16\):

\[
69 \times 16 = 1104
\]

Thus, the Length is:

\[
\text{Length} = \frac{1104}{551}
\]

Now we perform the division to find the approximate length:

\[
\text{Length} \approx 2.0 \text{ (when calculated)}
\]

Finally, rounding to the nearest tenth, the length of the popcorn box is approximately:

\[
\boxed{2.0} \text{ inches}
\]