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 surface area.A. 512 square unitsB. 1/2 square unitC. 8 square units

Answer 1

The answers are :

A. k = 8

B. k = 1/4

C. k = 1

EXPLANATION :

Note that dilation of surface areas :

`\begin{gathered} √(S_n)=k√(S_o) \\ k=\sqrt{(S_n)/(S_o)} \end{gathered}`

in which Sn is the new image

So is the original image

and k is the scale factor.

From the problem, we have So = 8 square units

A. Sn = 512 square units :

`\begin{gathered} k=\sqrt{(S_n)/(S_o)} \\ k=\sqrt{(512)/(8)} \\ k=8 \end{gathered}`

B. Sn = 1/2 square unit

`\begin{gathered} k=\sqrt{((1)/(2))/(8)} \\ k=(1)/(4) \end{gathered}`

C. Sn = 8 square units :

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