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

`\begin{gathered} a)64 \\ b)(1)/(16) \\ c)1 \end{gathered}`

Step-by-step 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=(A)/(8)`

a) When the surface area is 512 square units:

`\begin{gathered} k=(512)/(8) \\ k=64 \end{gathered}`

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

`\begin{gathered} k=((1)/(2))/(8) \\ k=(1)/(16) \end{gathered}`

c) When the surface area is 8 square units:

`\begin{gathered} k=(8)/(8) \\ k=1 \end{gathered}`