The ratio of radii of two cylinders is 1:2 and heights are 23 the ratio of their volumes is

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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

Answer

The ratio of radii of two cylinders is 1: 2 and heights are in the ratio 2:3. The ratio of their volumes is ______.

The ratio of radii of two cylinders is 1: 2 and heights are in the ratio 2:3. The ratio of their volumes is 1:6

Explanation:

Let r1, r2 be radii of two cylinders and h1, h2 be their heights.

Then `r_1/r_2 = 1/2` and `h_1/h_2 = 2/3`

Now, `V_1/V_2 = (pir^2 h_1)/(pir_2^2 h_2)`

= `(r_1/r_2)^2 xx h_1/h_2`

= `(1/2)^2 xx 2/3`

= `1/4 xx 2/3`

= `1/6`

= 1:6

Hence, `V_1 : V_2` = 1:6

Concept: Volume of a Cylinder

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