Question

a hollow metal sphere of internal and external radii 2cm and 4cm respectively is melted into a solid come of base 4cm. find the the height and slant height of the cone​

Answer 1

In the given sphere

R1 = 2cm and R2 = 4cm

We know that ,

Volume of sphere = 4 π ( R2cube - R1cube )

= 4 × 22 × [ 64 - 8]

3 × 7

= 4 × 22 × 56

21

= 704 cube.cm

3

If the sphere is now melted in a solid cone. Then also the volume will be the same

Therefore, the volume of cone = 704 by 3

Now,

the radius of base = 4cm

Volume of cone = π× Rsq× H

3

22 × 4 × H = 704

7 × 3 3

H = 704 × 7 × 3

88

H = 14 cm

(Slant height)^2 = H^2 + R^2

Slant height = ( 196 + 16) Sq root

= √212

Slant height = 14.56cm height = 14 cm