For a cone, the ratio between the volume and area of its base is 11 : 6. The height of the cone is :

1. $1\dfrac{5}{6}$ units

2. 5.5 units

3. 11 units

4. 5 units

Let radius of cone be r cm and height be h cm.

Given,

For a cone, the ratio between the volume and area of its base is 11 : 6.

$\Rightarrow \dfrac{\text{Volume of cone}}{\text{Area of base}} = \dfrac{11}{6} \\[1em] \Rightarrow \dfrac{\dfrac{1}{3}πr^2h}{πr^2} = \dfrac{11}{6} \\[1em] \Rightarrow \dfrac{h}{3} = \dfrac{11}{6} \\[1em] \Rightarrow h = \dfrac{11}{6} \times 3 \\[1em] \Rightarrow h = \dfrac{11}{2} = 5.5 \text{ units}.$

Hence, Option 2 is the correct option.