Question

Gabriel models the volume of a popcorn box as a right rectangular prism. Its dimensions are
3
3 in by
2, start fraction, 3, divided by, 4, end fraction
2
4/3
​
in by
5
5 in. How many cubic inches of popcorn would it hold when it is full? Round your answer to the nearest tenth if necessary.

Answer 1

To calculate the volume of a right rectangular prism (which is the shape of Gabriel's popcorn box), you can use the formula:

\[
\text{Volume} = \text{length} \times \text{width} \times \text{height}
\]

Given the dimensions of the popcorn box:

- Length = 3 inches
- Width = \(2 \frac{3}{4}\) inches = \(2 + \frac{3}{4} = \frac{8}{4} + \frac{3}{4} = \frac{11}{4}\) inches
- Height = 5 inches

Now plug in the values into the volume formula:

\[
\text{Volume} = 3 \times \frac{11}{4} \times 5
\]

First, calculate \(3 \times \frac{11}{4}\):

\[
3 \times \frac{11}{4} = \frac{33}{4}
\]

Now, multiply that by the height (5):

\[
\text{Volume} = \frac{33}{4} \times 5 = \frac{33 \times 5}{4} = \frac{165}{4}
\]

Next, divide 165 by 4:

\[
\frac{165}{4} = 41.25
\]

Thus, the volume of the popcorn box is approximately \(41.25\) cubic inches.

Now, rounding to the nearest tenth gives:

\[
\text{Volume} \approx 41.3 \text{ cubic inches}
\]

So, the popcorn box would hold approximately **41.3 cubic inches** of popcorn when it is full.