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:

If the radius of one cylinder is r then the radius of other cylinder is 2r i.e.

r₁ = r

r₂ = 2r

h₁ = h

h₂ = (3/2)h

Volume of Cylinder 1 = πr²h

Volume of Cylinder 2 = π(2r)²(3/2)(h) = 6 πr²h

Ratio of Volume of Cylinder 1 and Cylinder 2 = πr²h/6πr²h = 1:6

The correct answer is choice (a)

✦ Try This: The ratio of radii of two cylinders is 2: 1 and heights are in the ratio 3:2 The ratio of their volumes is (a) 6:1, (b) 9:1, (c) 3:1, (d) 9:2

If the radius of one cylinder is r then the radius of other cylinder is 2r i.e.

r₁ = r

r₂ = r/2

h₁ = h

h₂ = (2/3)h

Volume of Cylinder 1 = πr²h

Volume of Cylinder 2 = π(r/2)²(2/3)(h) = (1/6 )πr²h

Ratio of Volume of Cylinder 1 and Cylinder 2 = πr²h/(⅙)πr²h = 6:1

The correct answer is choice (a)

☛ Also Check: NCERT Solutions for Class 8 Maths Chapter 11

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NCERT Exemplar Class 8 Maths Chapter 11 Problem 24

The ratio of radii of two cylinders is 1: 2 and heights are in the ratio2:3. The ratio of their volumes is (a) 1:6 (b) 1:9 (c) 1:3 (d) 2:9

Summary:

The ratio of radii of two cylinders is 1: 2 and heights are in the ratio2:3. The ratio of their volumes is 1:6

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