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