2. Diameters of two cylinders are in the ratio of 2 : 3. Find the ratio of their heights if their volume is same.
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Answer:
Step-by-step explanation:
The diameter of two cylinders are in the ratio of 2:3.
Let the ratio be x
Diameter of first cylinder = 2x [ 2x/2 ]
Radius of first cylinder = x
Volume of first cylinder
= πr²h
= πx²h
Diameter of second cylinder = 3x
Radius of second cylinder = 1.5x [ 3x/2 ]
Volume of second cylinder
= πr²h
= π(1.5)²h
Volume of two cylinder are
→ πx²h : π(1.5)²h
→ h₁ : 2.25h₂
→ 100h₁ : 225h₂
→ h₁ : h₂ = 100 : 225
→ 20 : 45
→ 4 : 9
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