Question:
The ratio of radii of two cylinders is 1: 2 and heights are in the ratio 2:3. The ratio of their volumes is
(a) 1:6
(b) 1:9
(c) 1:3
(d) 2:9
Solution:
The correct answer is option (a) 1:6
Explanation:
Assume that r and R be the radii of the two cylinders and h and H be the height of the two cylinders
It is given that r/R = ½ and h/H = 2/3
We know that the volume of a cylinder = πr2 h
Now, v/V = πr2 h / πR2 H
v/ V = (r/R)2 (h/H)
v/V = (1/2)2 (2/3)
v/V = (1/4) (2/3) = 1/6
Therefore, the ratio of their volume is 1/6
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