The side lengths of two different cubes are 25 cm and 35 cm. What is the ratio of the volume of the smaller to the volume of the larger (in simplest form)?

(25/35)^3 = (5/7)^3

Volumes scale as the CUBES of corresponding lengths of similar figures

(25/35)^3 = (5/7)^3 = 125/343

thank you

You are welcome.

To find the ratio of the volume of the smaller cube to the larger cube, we need to calculate the volumes of both cubes and then compare the results.

The volume of a cube is given by the formula:

Volume = (side length)³

Let's calculate the volume of the smaller cube first:

Volume of the smaller cube = (25 cm)³ = 15625 cm³

Now let's calculate the volume of the larger cube:

Volume of the larger cube = (35 cm)³ = 42875 cm³

To find the ratio, we divide the volume of the smaller cube by the volume of the larger cube:

Ratio = Volume of the smaller cube / Volume of the larger cube

Ratio = 15625 cm³ / 42875 cm³

Now, we can simplify the ratio by dividing both the numerator and the denominator by their greatest common divisor (GCD), which is 625:

Ratio = (15625 cm³ / 625) / (42875 cm³ / 625)

Ratio = 25 / 68

Therefore, the ratio of the volume of the smaller cube to the volume of the larger cube, in simplest form, is 25/68.