If the right triangular prism is dilated usingĀ  a scale factor of 4, what would the volume of the dilated prism be? (1 point) H = 3 W = 4 L = 7

1 answer

To find the volume of the original right triangular prism, you can use the formula for the volume of a prism:

\[ \text{Volume} = \text{Base Area} \times \text{Height} \]

However, we first need to determine the area of the base of the prism, which is a right triangle. The base (area of triangle) can be calculated using the formula:

\[ \text{Area} = \frac{1}{2} \times \text{Width} \times \text{Length} \]

Given:

  • Width (W) = 4
  • Length (L) = 7

Calculating the base area:

\[ \text{Base Area} = \frac{1}{2} \times 4 \times 7 = \frac{28}{2} = 14 \]

Now, using the height (H = 3) to find the volume of the original prism:

\[ \text{Volume} = \text{Base Area} \times \text{Height} = 14 \times 3 = 42 \]

Now, when the prism is dilated with a scale factor of 4, all dimensions (length, width, and height) are multiplied by the scale factor.

The volume of a dilated prism can be calculated using the formula for dilation of volume, which is the original volume multiplied by the cube of the scale factor:

\[ \text{Dilated Volume} = \text{Original Volume} \times \text{Scale Factor}^3 \]

Thus:

\[ \text{Dilated Volume} = 42 \times 4^3 = 42 \times 64 = 2688 \]

Therefore, the volume of the dilated prism would be 2688 cubic units.