Question

Question is in the picture it’s a lot to type

Answer 1

1.

The ratio of their volumes is,

`\begin{gathered} \text{Ratio}=(108ft^3)/(4000ft^3) \\ =(27)/(1000) \end{gathered}`

Thus, the ratio of volume is 27:1000.

2.

The scale factor can be determined as,

`\begin{gathered} \text{Scale factor=(}(4000ft^3)/(108ft^3))^{(1)/(3)} \\ =10\colon3 \end{gathered}`

Thus, the scale factor is 10:3.

3.

The ratio of surface area is,

`\begin{gathered} \text{Ratio of surface area=(}(3)/(10))^2 \\ =9\colon100 \end{gathered}`

Thus, the ratio of surface area is 9:100.

4.

The surface area of the smaller cube can be determined as,

`\begin{gathered} (9)/(100)=(SA_(sc))/(SA_(bc)) \\ (9)/(100)=(SA_(sc))/(157ft^2) \\ SA_(sc)=14.13ft^2 \end{gathered}`

Thus, the surface area of the smaller cube is 14.13 square foot.