Question

What is the volume of a rectangular prism with a length of 4 2/3 ft., a height of 3 1/3ft., and a width of 2 1/2ft.? Write your answer as a mixed number or improper fraction.(1 point)

Answer 1

To find the volume of a rectangular prism, you can use the formula:

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

First, convert the mixed numbers to improper fractions:

1. For the length \(4 \frac{2}{3}\):
\[
4 \frac{2}{3} = \frac{4 \times 3 + 2}{3} = \frac{12 + 2}{3} = \frac{14}{3}
\]

2. For the height \(3 \frac{1}{3}\):
\[
3 \frac{1}{3} = \frac{3 \times 3 + 1}{3} = \frac{9 + 1}{3} = \frac{10}{3}
\]

3. For the width \(2 \frac{1}{2}\):
\[
2 \frac{1}{2} = \frac{2 \times 2 + 1}{2} = \frac{4 + 1}{2} = \frac{5}{2}
\]

Now substituting these values into the volume formula:

\[
\text{Volume} = \frac{14}{3} \times \frac{10}{3} \times \frac{5}{2}
\]

First, multiply the numerators:

\[
14 \times 10 \times 5 = 700
\]

Then, multiply the denominators:

\[
3 \times 3 \times 2 = 18
\]

Now combine these:

\[
\text{Volume} = \frac{700}{18}
\]

Next, simplify the fraction. Both 700 and 18 can be divided by 2:

\[
\frac{700 \div 2}{18 \div 2} = \frac{350}{9}
\]

Now convert \(\frac{350}{9}\) into a mixed number. Divide 350 by 9:

\[
350 \div 9 = 38 \quad \text{(whole number)}, \quad \text{remainder} = 350 - (9 \times 38) = 350 - 342 = 8
\]

Thus, we can express \(\frac{350}{9}\) as:

\[
38 \frac{8}{9}
\]

Therefore, the volume of the rectangular prism is:

\[
\boxed{\frac{350}{9}} \text{ or } \boxed{38 \frac{8}{9}} \text{ ft}^3
\]