Question

If the heights of two cylinders are in the ratio of 4 : 3 and their radii are in the ratio of 3 : 4 then what is the ratio of their volumes?

Answer 1

Given:-

• The heights of two cylinders are in the ratio of 4:3 and their radii are in the ratio of 3:4.

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To find:-

• Ratio of their volumes.

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Solution:-

Here,

• Ratio of height = 4:3
• Ratio of radii = 3:4

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According to the question,

⇛ π(3)² × 4 : π(4)² × 3

⇛ 9 × 4 : 16 × 3

⇛ 36:48

⇛ 9:12

⇛ 3:4

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Hence,

• the ratio of their volumes is 3:4.

Answer 2

Ratio of radius of Cylinder1 to that of cylinder2 = 3:2 (given)

=> radius of cylinder1 = 3x unit

& radius of cylinder2 = 2x unit

Ratio of their heights = 4:3 (given)

=> height of cylinder1 = 4y unit

& height of cylinder2 = 3y unit

Hence volume of cylinder1 = pi (3x)² * 4y . . .(1)

Volume of cylinder2 = pi(2x)² * 3y . . . . (2)

Hence, Volume ratio = (pi* 9x² *4y) /( pi * 4x² *3y)

=> 36pi/12pi

=> 3:1

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