The radii and height of two cylinders are in the ratio 3:2 and 4:5 respectively. Find the ratio of their volumes A)9:5 B)18:10 C)21:25 D)8:3
Question
The radii and height of two cylinders are in the ratio 3:2 and 4:5 respectively. Find the ratio of their volumes A)9:5 B)18:10 C)21:25 D)8:3
Solution
The volume of a cylinder is given by the formula V = πr²h, where r is the radius and h is the height.
Given that the radii and heights of the two cylinders are in the ratios 3:2 and 4:5 respectively, we can represent the radii as 3x and 2x, and the heights as 4y and 5y for some values of x and y.
The volume of the first cylinder (V1) is therefore π*(3x)²*(4y) = 36πxy.
The volume of the second cylinder (V2) is π*(2x)²*(5y) = 20πxy.
The ratio of the volumes V1:V2 is therefore 36πxy : 20πxy = 36:20 = 9:5.
So, the answer is A) 9:5.
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