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Question
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
The radius and height of a cylinder are in the ratio 3 : 2.
Let the radius be 3x and height be 2x. Then,
Volume of a cylinder = 19404 cm3 ...[Given]
∵ Volume of a cylinder = πr2h
∴ `19404 = 22/7 xx (3x)^2 xx (2x)`
⇒ `19404 = 22/7 xx 9x^2 xx 2x = (22 xx 18x^3)/7`
⇒ `19404 = (396x^3)/7`
⇒ x3 = 343
⇒ x3 = (7)3
∴ x = 7 cm
Hence, radius of the cylinder = 3 × 7 = 21 cm
And height of the cylinder = 2 × 17 = 14 cm
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