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?

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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?

Mathematics
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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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.
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

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