Question

Two similar solids have a scale factor of 3:4. What is the ratio of their volumes, expressed in lowest terms? Enter your answer in the boxes.

Answer 1

For this case, what you should know is that if the object is similar, then to find its volume you must raise the scale factor to the cube.
 We have then:
 (3/4) ^ 3 = ((3 ^ 3) / (4 ^ 3)) = (9) / (64)
 answer
 the ratio of their volumes, expressed in lowest terms is
 9:64

Answer 2

Answer:

The ratio of their volumes is:  27:64.

Step-by-step explanation:

We have been given scale factor of two similar solids which is 3:4

And volume of similar solid is related to the scale factor of similar solid as:

$\text{Ratio of Volume}= \text{scale factor}^3$

$\text{Ratio of Volume}=(\frac{3}{4})^3$

$\text{Ratio of Volume}=\frac{3^3}{4^3}$

$\text{Ratio of Volume}=\frac{27}{64}$

So, the ratio of their volumes is:  27:64.