Find the diameter of a cone whose volume and height are 3696 cubic units and 18 units, respectively. (Use π =$$\frac{22}7$$​ )

Correct option is A

​Given:

Volume of the cone = 3696 cubic units

Height of the cone = 18 units

Formula Used:

Volume of cone = $$\frac{1}{3} \pi r^2 h$$​​

Solution:

Substitute the known values into the formula:

​$$3696 = \frac{1}{3} \times \frac{22}{7} \times r^2 \times 18​$$​​

​$$3696 = \frac{1}{3} \times \frac{22}{7} \times 18 \times r^2$$​​

​$$3696 = \frac{22 \times 18}{21} \times r^2$$​​

​$$3696 = \frac{396}{21} \times r^2$$​​

​$$\implies r^2 = \frac{3696 \times 21}{396} = 196 ​$$​​

​$$r = \sqrt{196} = 14 \, \text{units}$$​​

The diameter is 2r:

Diameter = 2 × 14 = 28 units