Question

A solid with surface area 8 square units is dilated by a scale factor of k to obtain a solid with surface area A square units. Find the value of k which leads to an image with each given surface area.a. 512 square unitsk =b. 1/2 square unitk =c. 8 square unitsk =

Answer 1

ANSWER

$\begin{gathered} a)64 \\ b)\frac{1}{16} \\ c)1 \end{gathered}$

EXPLANATION

The scale factor k of dilation is gotten by dividing the surface area of the dilated image by the surface area of the pre-image.

That is:

$k=\frac{A}{8}$

a) When the surface area is 512 square units:

$\begin{gathered} k=\frac{512}{8} \\ k=64 \end{gathered}$

b) When the surface area is 1/2 square unit:

$\begin{gathered} k=\frac{\frac{1}{2}}{8} \\ k=\frac{1}{16} \end{gathered}$

c) When the surface area is 8 square units:

$\begin{gathered} k=\frac{8}{8} \\ k=1 \end{gathered}$