Question

imagine that a rectangular prism similar to the one shown has a scale factor of 1/2. what is the volume of the new rectangular prism?
6 cm / 5 cm / 4 cm on all 4 sides
a. 60 cm^3
b. 30 cm^3
c. 120 cm^3
d. 15 cm^3

Answer 1

To find the volume of the original rectangular prism, we can use the formula for the volume of a rectangular prism:

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

Given dimensions are 6 cm, 5 cm, and 4 cm. Let's calculate the volume of the original prism:

\[
V = 6 \, \text{cm} \times 5 \, \text{cm} \times 4 \, \text{cm}
\]
\[
V = 120 \, \text{cm}^3
\]

Now, since the new rectangular prism has a scale factor of \( \frac{1}{2} \), the dimensions of the new prism will be:

- Length = \( 6 \times \frac{1}{2} = 3 \, \text{cm} \)
- Width = \( 5 \times \frac{1}{2} = 2.5 \, \text{cm} \)
- Height = \( 4 \times \frac{1}{2} = 2 \, \text{cm} \)

Now we can calculate the volume of the new rectangular prism:

\[
V_{new} = \text{length} \times \text{width} \times \text{height}
\]
\[
V_{new} = 3 \, \text{cm} \times 2.5 \, \text{cm} \times 2 \, \text{cm}
\]
\[
V_{new} = 3 \times 2.5 \times 2
\]
\[
V_{new} = 15 \, \text{cm}^3
\]

Hence, the volume of the new rectangular prism is **15 cm³**.

The correct answer is:
d. 15 cm³