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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

Solution:

A figure is drawn below to visualize the shapes.

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

As three metallic spheres are melted and recast into a single solid sphere, the sphere formed by recasting these three spheres will have the same volume equal to the sum of the volumes of the three spheres.

Volume of the resulting sphere = Sum of the volumes of three spheres

We will find the volume of the sphere by using formula;

Volume of the sphere = 4/3πr3where r is the radius of the sphere

Radius of 1st sphere, r₁ = 6 cm

Radius of 2nd sphere, r₂ = 8 cm

Radius of 3rd sphere, r₃ = 10 cm

Let the radius of the resulting sphere be r.

Volume of the resulting sphere = Sum of the volumes of three spheres

4/3 πr3 = 4/3 πr₁3 + 4/3 πr₂3 + 4/3 πr₃3

r3 = [r₁3 + r₂3 + r₃3]

r3 = [(6 cm)3 + (8 cm)3 + (10 cm)3]

r3 = [216 cm3 + 512 cm3 + 1000 cm3]

r3 = 1728 cm3

r = 12 cm

Therefore, the radius of the sphere so formed will be 12 cm.

☛ Check: NCERT Solutions Class 10 Maths Chapter 13

Video Solution:

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.

NCERT Solutions for Class 10 Maths Chapter 13 Exercise 13.3 Question 2

Summary:

The radius of the single solid sphere resulting from melting three metallic spheres of radii 6 cm, 8 cm, and 10 cm respectively is 12 cm.

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