Three solid spheres of iron whose diameters are 2 cm, 12 cm and 16 cm . . .

Question : Three solid spheres of iron whose diameters are 2 cm, 12 cm and 16 cm , respectively, are melted into a single solid sphere. Find the radius of the new solid sphere?

Doubt by Mehak 

Solution : 

Let 

R = Radius of the New Sphere

r₁ = 2/2 = 1 cm

r₂ = 12/2 = 6 cm

r₃ = 16/2 = 8 cm 

We know, when solid are melted and recasted then their volume remains same. 

Volume of Three solid spheres = Volume of Bigger Solid Sphere

V₁ + V₂ + V₃ = V

(4/3)πr₁³ + (4/3)πr₂³ + (4/3)πr₃³ = (4/3)πR³

(4/3)π(r₁³+r₂³+r₃³) = (4/3)πR³

1³+6³+8³ = R³
1+216+512 = R³

729 = R³

(9)³=R³

9 = R

R = 9 cm

Hence, Radius of the new solid sphere would be 9 cm