Question

A 3-D figure is dilated by a scale factor of 13 . Determine which statement is true about the new dilated surface area.(1 point)ResponsesThe surface area will be 9 times as large as the original.The surface area will be 9 times as large as the original.The surface area will be 13 the size of the original.The surface area will be  Start Fraction 1 over 3 End Fraction the size of the original.The surface area will be 3 times as large as the original.The surface area will be 3 times as large as the original.The surface area will be 19 the size of the original.

Answer 1

When a 3-D figure is dilated by a scale factor \( k \), the new surface area is scaled by \( k^2 \). In this case, the scale factor is 13.

To find the new surface area relative to the original, calculate \( k^2 \):

\[ k^2 = 13^2 = 169 \]

Thus, the new surface area will be 169 times the size of the original surface area.

Based on the given responses, none of them state that the surface area will be 169 times as large as the original, which would have been the correct answer.

Therefore, none of the provided statements are true.