Question

What is the volume, in cubic feet, of a rectangular prism with a height of 2 1/2 ft., a length of 2 1/4 ft., and a width of 3 1/8 ft.? Your answer should be a mixed number in simplest form.(1 poin (all numbers are fractions)

Answer 1

To find the volume of a rectangular prism, you multiply its height, length, and width. The formulas is:

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

First, let's convert the mixed numbers to improper fractions:

1. Height: \( 2 \frac{1}{2} = \frac{5}{2} \) (since \( 2 \times 2 + 1 = 5 \))
2. Length: \( 2 \frac{1}{4} = \frac{9}{4} \) (since \( 2 \times 4 + 1 = 9 \))
3. Width: \( 3 \frac{1}{8} = \frac{25}{8} \) (since \( 3 \times 8 + 1 = 25 \))

Now, we multiply these improper fractions together:

\[
\text{Volume} = \frac{5}{2} \times \frac{9}{4} \times \frac{25}{8}
\]

We can multiply the numerators and the denominators:

\[
= \frac{5 \times 9 \times 25}{2 \times 4 \times 8}
\]

Calculating the numerator:

\[
5 \times 9 = 45
\]

\[
45 \times 25 = 1125
\]

Calculating the denominator:

\[
2 \times 4 = 8
\]

\[
8 \times 8 = 64
\]

So, we have:

\[
\text{Volume} = \frac{1125}{64}
\]

Next, we convert this improper fraction to a mixed number.

Dividing \( 1125 \) by \( 64 \):

\[
1125 \div 64 = 17 \text{ R } 37
\]

This means that \( 1125 = 64 \times 17 + 37 \). Therefore, the mixed number is:

\[
17 \frac{37}{64}
\]

The fraction \( \frac{37}{64} \) is already in simplest form because \( 37 \) is a prime number and does not divide \( 64 \).

Thus, the volume of the rectangular prism is:

\[
\boxed{17 \frac{37}{64}} \text{ cubic feet.}
\]