Question

a solid metallic sphere of diameter 21 cm is melted and recast into a number of smaller cones, each of diameter 7 cm and height 3 cm. find the number of cones formed.

Answer 1

Solution:-

Diameter of sphere = 21 cm 
So, radius of the sphere = 21/2 = 10.5 cm
Volume of sphere = 4/3πr³
= 4/3*22/7*10.5³
= 4851 cu cm
Now, 
Diameter of the cone so formed = 7 cm
So, radius of the cone = 7/2 = 3.5 cm
Volume of cone = 1/3πr²h
= 1/3*22/7*3.5*3.5*3
= 38.5 cu cm
Number of cones formed = 4851/38.5
= 126 cones
Answer.