Two similar cylinders have radii of 7 and 1, respectively. What is the ratio of their volumes?A.343:1B.112:1C.35.35:1D.49:1SUBMITarrow_backPREVIOUS
Question
Two similar cylinders have radii of 7 and 1, respectively. What is the ratio of their volumes?A.343:1B.112:1C.35.35:1D.49:1SUBMITarrow_backPREVIOUS
Solution
The volume of a cylinder is given by the formula V = πr²h, where r is the radius and h is the height.
Since the cylinders are similar, their heights are proportional to their radii, so we can say that the height of the first cylinder is 7h and the height of the second cylinder is h.
The volume of the first cylinder is V1 = π(7)²(7h) = 343πh.
The volume of the second cylinder is V2 = π(1)²(h) = πh.
The ratio of their volumes is V1 : V2 = 343πh : πh = 343 : 1.
So, the answer is A. 343:1.
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