A cylinder has a radius of 3 cm and a length of 10 cm. Every dimension of the cylinder is multiplied by 3 to form a new cylinder. How is the ratio of the volumes related to the ratio of corresponding dimensions?

Question

A cylinder has a radius of 3 cm and a length of 10 cm. Every dimension of the cylinder is multiplied by 3 to form a new cylinder. How is the ratio  of the volumes related to the ratio of corresponding dimensions?

directrix · Answer

If two solids are similar, the cube of the scale factor of the two solids is equal to the ratio of the volumes.

The scale factor for the two cylinders is 1 to 3 because each measure of the first cylinder was multiplied by 3 to get the second cylinder.

directrix · Answer

Applying the theorem, cube the ratio (1/3) to get the ratio of the two volumes.

The ratio of the volumes is 1:27. @Autumn_greined