The ratio of radii of two cylinders is 1: 2

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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