Question

a solid sphere of radius 7cm is melted to form cones of radius 7/2 cm and height 7/2 cm. find the number of cones formed?

Answer 1

The right answer is 32 cones are formed.

Answer 2

let no of cones formed be x.

volume of sphere = 4/3 πr³

volume of 1 cone = 1/3 πr²h

we know , that
sphere was melted and reformed into number of cones

so ,
number of cones × volume of 1 cone = volume of sphere

=> x × 1/3 πr²h = 4/3 πr³

=> x × r²h = 4 × r³

(since , π and 3 got cancelled out)

=> x × 7/2 × 7/2 × 7/2 = 4 × 7 × 7 × 7

=> x = 4 × 7 × 7 × 7 × 2/7 × 2/7 × 2/7

=> x = 4 × 2 × 2 × 2 = 32


hence , number of cones formed = 32


hope this helps