A cube

A cube has a surface area of 64 ft². Hedy creates a reduction of this cube using a scale factor of 0.5.

What is the surface area of the reduction?

Correct answer:

S₂ =  16 ft²

Step-by-step explanation:

$$\begin{gathered} S_1=64{\text{ft}}^2 \\ {S}_1=6a^2 \\ a=\sqrt{S_1/6}=\sqrt{64/6}\doteq 3.266\text{ft} \\ k=0.5 \\ b=a\cdot k=3.266\cdot 0.5\doteq 1.633\text{ft} \\ {S}_2=6\cdot b^2=6\cdot 1.633^2=16=16{\text{ft}}^2 \\ \text{ Verifying Solution: } \\ {S}_2=k^2\cdot S_1 \end{gathered}$$

Try another example