Question

What is the similarity ratio of a cube with volume 729m^3 to a cube with volume 3375 m^3

Answer 1

Answer:

3/5

Step-by-step explanation:

We are to find the similarity ratio of a cube with volume  $729 m^3$ to a cube with volume $3375 m^3$.

We know the formula for the ratio of two cubes:

$\frac{V_1}{V_2} =k^3$

where $k$ is the similarity ratio of the two cubes.

Substituting the given values in the formula to find $k$:

$k^3 = \frac {729} {3375}$

$k^3 = \frac {27} {125}$

$k^3 = (\frac {27} {125})^3$

$k=\frac{3}{5}$

Therefore, the similarity ratio of the two cubes is 3/5.

Answer 2

Answer:

The similitary ratio is 3:5

Step-by-step explanation:

To answer this question let's call:

$V_1 = 729\ m^3$ to volume 1.

Let's call:

$V_2 = 3375\ m^3$ to volume 2

The relation k of simiiltud between both volumes we find dividing $V_1$ between $V_2$

$\frac{V_1}{V_2} = k^3\\\\\frac{V_1}{V_2} = \frac{729m^3}{3375m^3}\\\\\frac{V_1}{V_2} = \frac{27}{125}\\\\\frac{V_1}{V_2} = \frac{3^3}{5^3}\\\\k^3 = (\frac{3}{5})^3\\\\k = \frac{3}{5}$