Question

A right rectangular prism has a length of 1/3 m, a width of 1/4 m, and a height of 2 1/2m. Use the formula method to find the volume of the prism, reduce the answer to the lowest terms

Answer 1

To find the volume \( V \) of a right rectangular prism, we use the formula:

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

Given the dimensions:
- Length \( l = \frac{1}{3} \) m
- Width \( w = \frac{1}{4} \) m
- Height \( h = 2 \frac{1}{2} \) m

First, we need to convert the height \( 2 \frac{1}{2} \) m to an improper fraction:

\[
2 \frac{1}{2} = 2 + \frac{1}{2} = \frac{4}{2} + \frac{1}{2} = \frac{5}{2} \text{ m}
\]

Now we substitute the values into the volume formula:

\[
V = \left( \frac{1}{3} \right) \times \left( \frac{1}{4} \right) \times \left( \frac{5}{2} \right)
\]

Next, we multiply the fractions:

1. Multiply the numerators:
\[
1 \times 1 \times 5 = 5
\]

2. Multiply the denominators:
\[
3 \times 4 \times 2 = 24
\]

So we have:

\[
V = \frac{5}{24} \text{ m}^3
\]

The fraction \( \frac{5}{24} \) is already in its lowest terms. Thus, the volume of the prism is:

\[
\boxed{\frac{5}{24}} \text{ m}^3
\]