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The radius and height of a cylinder are in the ratio 3:2 and its volume is 19,404 cm³. Find its radius and height.

Solution:

If r = radius of the cylinder and,

h = height of the cylinder

Then r/h = 3/2

Volume = πr²h = 19,404

πr²h = 19,404

h = 2r/3

Volume = (22/7) × r² × (2r/3) = 19404

r³= (19404/22) × (3/2) × 7

r³ = (1764/2) × (3/2) × 7

r³ = 441 × 3 × 7

r³ = 3 × 7 × 3 × 7 × 3 × 7

r = 3 × 7 = 21cm

Therefore,

h = 2r/3 = 21 × (⅔) = 14cm

✦ Try This: The radius and height of a cylinder are in the ratio 7:1 and its curved surface area is 2816 cm². Find its radius and height.

If r = radius of the cylinder and,

h = height of the cylinder

Then r/h = 7/1

Volume = 2πrh = 2816

2πrh = 2816

h = r/7

Curved Surface Area = 2 × (22/7) × r × (r/7) = 2816

r² = 1/2 × (2816/22) × (7) × 7

r² = (128/2) × (7) × 7

r² = 64 × 7 × 7

r² = 8 × 8 × 7 × 7

r = 8 × 7 = 56m

Therefore,

h = r/7 = 56 × (1/7) = 8 cm

Hence the radius and height of the cylinder are 56cm and 8 cm

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

NCERT Exemplar Class 8 Maths Chapter 11 Problem 90

The radius and height of a cylinder are in the ratio 3:2 and its volume is 19,404 cm³. Find its radius and height.

Summary:

The radius and height of a cylinder are in the ratio 3:2 and its volume is 19,404 cm³. The radius and height.of the cylinder 21 cm and 14 cm respectively

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