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The ratio of height and radius of a right circular cone is 7 : 6 and it's volume is 264 dm3.then, find the diameter.
1. 20 dm
2. 16 dm
3. 12 dm
4. 19 dm

1 Answer

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Correct Answer - Option 3 : 12 dm

Given

Ratio of height and radius of cone = 7 : 6

Volume of cone = 264 dm3

Formula used

Volume of cone = (1/3)πr2h

Where r and h are radius and height respectively, 

Calculation

Height = 7x

Radius = 6x

264 = (1/3) × (22/7) × 6x × 6x × 7x

⇒ (264 × 3 × 7)/(22 × 6 × 6 × 7) = x

⇒ 22/22 = x

⇒ 1 = x

Radius = 6(1)

⇒ 6 dm

Diameter= 2 radius

⇒ 2(6)

⇒ 12 dm

∴ The diameter of the cone is 12 dm

 

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