# Diameters of two cylinder are in the ratio of 2:3 find the ratio of their heights if their volume are same.

2
by brai1

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by brai1

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r=d/2

r1=2x/2=x (h1)

r2=3x/2 (h2)

22/7*x*x*h1 = 22/7*3x/2 * 3x/2 *h2

h1=3x/2*3x/2*1/x*1/x*h2

h1=3/2*3/2*h2

h1=9/4h2

4h1=9h2

so 4:9 is the required ratio

⇒ r1 = 2x

r2 = 3x

Given that volumes are also equal

⇒ π(r1²)h1 = π(r2²)h2

⇒ (2x)² h1 = (3x)²h2

⇒ 4x² h1 = 9x² h2

⇒ h1/h2 = 9x²/4x²

⇒ h1/h2 = 9/4

∴The ratio of the heights = 9:4