Suppose a rectangular prism is dilated with a scale factor of 3. If the original rectangular prism has a surface area of 4 in.^2, what would be the surface area of the new dilated rectangular prism?

__ in.^2

1 answer

When a three-dimensional shape, such as a rectangular prism, is dilated, the surface area is affected by the square of the scale factor.

Given:

  • Original surface area = \( 4 , \text{in}^2 \)
  • Scale factor = \( 3 \)

The formula for the surface area of the dilated shape is:

\[ \text{New Surface Area} = \text{Original Surface Area} \times (\text{Scale Factor})^2 \]

Substituting the known values:

\[ \text{New Surface Area} = 4 \times 3^2 = 4 \times 9 = 36 , \text{in}^2 \]

Therefore, the surface area of the new dilated rectangular prism is \( \boxed{36} , \text{in}^2 \).