Question

Ana finds the volume of a right rectangular prism with a length of 1/2 cm, width 1 1/2cm and a height of 2 cm using the cube method, what answer should she get, provide the volume of the prism as an improper fraction reduced to the lowest terms

Answer 1

To find the volume of a right rectangular prism, the formula is given by:

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

Given the dimensions:
- Length = \( \frac{1}{2} \) cm
- Width = \( 1 \frac{1}{2} \) cm = \( \frac{3}{2} \) cm (as \( 1 \frac{1}{2} = 1 + \frac{1}{2} = \frac{2}{2} + \frac{1}{2} = \frac{3}{2} \))
- Height = \( 2 \) cm

Now, let's calculate the volume step by step.

1. Convert the dimensions into improper fractions:
- Length = \( \frac{1}{2} \)
- Width = \( \frac{3}{2} \)
- Height = \( 2 = \frac{2}{1} \)

2. Multiply the dimensions together:
\[
\text{Volume} = \frac{1}{2} \times \frac{3}{2} \times \frac{2}{1}
\]

3. First, multiply \( \frac{1}{2} \) and \( \frac{3}{2} \):
\[
\frac{1}{2} \times \frac{3}{2} = \frac{1 \times 3}{2 \times 2} = \frac{3}{4}
\]

4. Now multiply this result by \( \frac{2}{1} \):
\[
\frac{3}{4} \times \frac{2}{1} = \frac{3 \times 2}{4 \times 1} = \frac{6}{4}
\]

5. Simplify \( \frac{6}{4} \):
\[
\frac{6}{4} = \frac{3}{2} \text{ (by dividing the numerator and denominator by 2)}
\]

Thus, the volume of the prism, as an improper fraction reduced to the lowest terms, is:

\[
\boxed{\frac{3}{2}} \, \text{cm}^3
\]