# 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

1. 2 cm
2.  3 cm
3.  4 cm
4.  6 cm

Anurag Mishra Professor Asked on 19th July 2015 in

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 r3/3
Where, r = radius of the ball
Now, the volume of spherical ball = 4 x 22 x 33/3 x 7 = 88 x 9/7 = 792/7 cm3The volume of spherical ball = the volume of cone            (According to the question)
Formula-
The volume of cone = Pai x r2 x h/3
Where, 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.

Anurag Mishra Professor Answered on 19th July 2015.