Question

Metallic spheres of radii 6 cm, 8 cm and 10 cm, respectively are melted to form a single solid sphere. Find the radius of the resulting sphere.

Answer 1

We have,

the radii r₁ = 6 cm, r2 = 8 and r3 = 10 cm

Let the radius of the resulting sphere be R. 

As,

Volume of resulting sphere = Volume of three metallic spheres 

`rArr 4/3piR^3 = 4/3pir_1^3 +4/3pir_2^3 +4/3pir_3^3`

`rArr 4/3piR^3 = 4/3pi(r_1^3 + r_2^3 + r_3^3)`

`rArr R^3 = r_1^3 + r_2^3 + r_3^3`

`rArr R^3 = 6^3 +8^3 + 10^3`

`rArr R^3 =216 + 512+1000`

`rArr R^3 =1728`

`rArr R = root(3)(1728)`

`rArr R= 12  "cm"`

So, the radius of the resulting sphere is 12 cm.