# Find The Height Of The Cone With Diameter Of The Base

A solid metallic spherical ball of diameter 6 cm is melted and recast into a cone with diameter of the base as 12 cm. The height of the cone is

- 2 cm
- 3 cm
- 4 cm
- 6 cm

**Answer: (2) 3 cm**

**Explanation:-**

The diameter of solid metallic ball = 6 cm (Given)

Then, the radius of this ball = 6 /2 = 3 cm

**Formula-**

**The volume of solid metallic ball = 4 x pai x r ^{3}/3**

Where, r = radius of the ball

Now, the volume of spherical ball = 4 x 22 x 3

^{3}/3 x 7 = 88 x 9/7 = 792/7 cm

^{3}The volume of spherical ball = the volume of cone (According to the question)

**Formula-**

**The volume of cone = Pai x r**

^{2}x h/3Where, r = radius of the cone & h = height of the cone.

The diameter of the cone = 12 cm (Given)

Then, the radius of the cone (r) = 12/2 = 6 cm

Now, the volume of the cone = 22 x (6)

^{2}x h/3 x 7 = 792/7

22 x 6 x 2 x h/7 = 4 x 22 x 3 x 3/7

h = 3 cm

Hence, the height of the cone is (2) 3 cm.