A hollow sphere of external and internal diameters of 8 cm and 4 cm respectively is melted and made into another solid in the shape of a right circular cone of base diameter of 8 cm. find the height of the cone.

Answers (1)

Voume of hollow sphere= frac43*prod *(r_0^3-r_i^3) ; ; ; where; r_0 ; is ;external ; radius, ;r_i ;is ;inner ; radius

Voume of hollow sphere=frac43*prod *(4^3-2^3) ; ; ; equation(1)

Voume of right circular cone=frac13*prod *r^2*h ; ; ; ; where ; r ; is ; radius ; of ; cone ; and ; h ; is; height; of; cone;

Voume of right circular cone=frac13*prod *4^2*h ; ; ; ; ; ; ; equation(2)

From equation(1) and equation(2)

frac43*prod *(4^3-2^3)=frac13*prod*4^2*h

Rightarrow 4 *(4^3-2^3)=16*h

Rightarrow 64-8=4*h

Rightarrow 56=4*h

Rightarrow h=14

Height of cone is 14 cm

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