Question

a 3 - d figure is dilated by a scale factor of $\frac{1}{3}$. determine which statement is true about the new dilated surface area. (1 point)
the surface area will be 3 times as large as the original.
the surface area will be $\frac{1}{9}$ the size of the original.
the surface area will be 9 times as large as the original.
the surface area will be $\frac{1}{3}$ the size of the original.
check answer remaining attempts : 3

Explanation:

Step1: Recall the formula for surface - area dilation

If a 3 - D figure has a scale factor \(k\) for dilation, the formula for the ratio of the new surface area \(S_{new}\) to the original surface area \(S_{old}\) is \(S_{new}=k^{2}S_{old}\). Here, \(k = \frac{1}{3}\).

Step2: Calculate \(k^{2}\)

Substitute \(k=\frac{1}{3}\) into the formula \(k^{2}\). We get \(k^{2}=(\frac{1}{3})^{2}=\frac{1\times1}{3\times3}=\frac{1}{9}\).

Answer:

The surface area will be \(\frac{1}{9}\) the size of the original.