Question

imagine that a retangular prism is similar to the one shown has a scale factor of 1/2. what is the volume of the new prism? volume = cm^3 W = 7 L = 6 H = 7

Answer 1

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

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

In the given prism, we have:

- Width \( W = 7 \) cm
- Length \( L = 6 \) cm
- Height \( H = 7 \) cm

First, we calculate the volume of the original prism:

\[
\text{Volume} = W \times L \times H = 7 \times 6 \times 7
\]

Calculating the above:

\[
7 \times 6 = 42
\]

Then multiply that result by the height:

\[
42 \times 7 = 294 \text{ cm}^3
\]

Now that we have the volume of the original prism, we need to find the volume of the new prism with a scale factor of \( \frac{1}{2} \). The volume scale factor is the cube of the linear scale factor. Therefore, we calculate it as follows:

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

Now, we multiply the volume of the original prism by the volume scale factor:

\[
\text{Volume of new prism} = \text{Original Volume} \times \text{Volume Scale Factor}
\]

\[
\text{Volume of new prism} = 294 \times \frac{1}{8} = \frac{294}{8} = 36.75 \text{ cm}^3
\]

Thus, the volume of the new prism is:

\[
\text{Volume of new prism} = 36.75 \text{ cm}^3
\]