Question

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

Answer 1

1.

The ratio of their volumes is,

$\begin{gathered} \text{Ratio}=\frac{108ft^3}{4000ft^3} \\ =\frac{27}{1000} \end{gathered}$

Thus, the ratio of volume is 27:1000.

2.

The scale factor can be determined as,

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

Thus, the scale factor is 10:3.

3.

The ratio of surface area is,

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

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

4.

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

$\begin{gathered} \frac{9}{100}=\frac{SA_{sc}}{SA_{bc}} \\ \frac{9}{100}=\frac{SA_{sc}}{157ft^2} \\ SA_{sc}=14.13ft^2 \end{gathered}$

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