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.

1 answer

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

Given that the original surface area of the rectangular prism is 4 in² and the scale factor of dilation is 3, the new surface area can be calculated as follows:

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

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

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

\[ \text{New Surface Area} = 36 , \text{in}^2 \]

Therefore, the surface area of the new dilated rectangular prism is 36 in².