cube one V=512m

Question

cube two V=1728m
The two cubes are similar in shape. Compare the volume of the two and determine the scale factor from the smaller cube to the larger cube. Enter your response as a fraction. (1 point)

Answer 1

To determine the scale factor from the smaller cube to the larger cube, we first need to find the ratio of their volumes.

The volume of cube one, $V_1=512,{\text{m}}^3$.

The volume of cube two, $V_2=1728,{\text{m}}^3$.

The ratio of the volumes of the two cubes is:

$$\text{Volume Ratio}=\frac{V_2}{V_1}=\frac{1728}{512}$$

Now, we can simplify this fraction:

$$\frac{1728÷512}{512÷512}=\frac{3.375}{1}=\frac{27}{8}$$

The volumes of similar shapes relate to the scale factor (k) by the formula:

$${\left(\text{Scale Factor}\right)}^3=\frac{V_2}{V_1}$$

So, we have:

$$k^3=\frac{27}{8}$$

Taking the cube root of both sides to find the scale factor $k$:

$$k=\sqrt[3]{\frac{27}{8}}=\frac{\sqrt[3]{27}}{\sqrt[3]{8}}=\frac{3}{2}$$

Thus, the scale factor from cube one to cube two is:

$$\frac{3}{2}$$

Final Answer: $\frac{3}{2}$