If two cylinders are similar and the ratio between the lengths of their edges is 4:3, what is the ratio of their volumes?A.16:27B.4:3C.16:9D.64:27SUBMITarrow_backPREVIOUS
Question
If two cylinders are similar and the ratio between the lengths of their edges is 4:3, what is the ratio of their volumes?A.16:27B.4:3C.16:9D.64:27SUBMITarrow_backPREVIOUS
Solution
The volume of a cylinder is given by the formula V=πr²h, where r is the radius and h is the height. If two cylinders are similar, their radii and heights are in the same ratio.
Given that the ratio of the lengths of their edges (which includes radius and height) is 4:3, the ratio of their volumes is the cube of the ratio of their edges.
So, the ratio of their volumes is (4:3)³ = 64:27.
Therefore, the answer is D. 64:27.
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