Question

Imagine that a rectangular prism similar to the one shown has a scale factor 1/2. What is the volume of the new rectangular prism?
the cylinder prism shown has a length of 7cm, a width if 6cm, and a height of 4cm

Answer 1

To find the volume of the original rectangular prism, you can use the formula for the volume of a rectangular prism, which is:

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

For the given dimensions:
- Length = 7 cm
- Width = 6 cm
- Height = 4 cm

Calculating the volume of the original prism:

\[
\text{Volume} = 7 \, \text{cm} \times 6 \, \text{cm} \times 4 \, \text{cm} = 168 \, \text{cm}^3
\]

Now, since the new rectangular prism is similar to the original one with a scale factor of \( \frac{1}{2} \), the volume of similar shapes scales by the cube of the scale factor:

\[
\text{Volume scale factor} = \left( \frac{1}{2} \right)^3 = \frac{1}{8}
\]

Thus, to find the volume of the new rectangular prism, multiply the volume of the original prism by the volume scale factor:

\[
\text{Volume of new prism} = 168 \, \text{cm}^3 \times \frac{1}{8} = 21 \, \text{cm}^3
\]

Therefore, the volume of the new rectangular prism is **21 cm³**.