A metallic sphere of radius 4.2 cm is melted and recast into the shape of a cylinder of radius 6 cm. Find the height of the cylinder

Solution:

A figure is drawn to visualize the shapes according to the given question.

As a metallic sphere is melted and recast into the shape of a cylinder, their volume must be the same.

Volume of the sphere = Volume of the cylinder

Let us find the volume of the sphere and cylinder by using formulae;

Volume of the sphere = 4/3πr³ where r is the radius of the sphere

Volume of the cylinder = πr²h where r and h are radius and height of the cylinder respectively

Radius of the sphere, r₁ = 4.2 cm

Radius of the cylinder, r₂ = 6 cm

Let the height of the cylinder be h.

Volume of sphere = Volume of cylinder

4/3πr₁³ = πr₂²h

(4/3)r₁³ = r₂²h

h = 4r₁³ / 3r₂²

= (4 × 4.2 cm × 4.2 cm × 4.2 cm) / (3 × 6 cm × 6 cm)

= 2.744 cm

Hence, the height of the cylinder so formed will be 2.744 cm.

☛ Check: NCERT Solutions for Class 10 Maths Chapter 13

Video Solution:

A metallic sphere of radius 4.2 cm is melted and recast into the shape of a cylinder of radius 6 cm. Find the height of the cylinder.

NCERT Solutions for Class 10 Maths Chapter 13 Exercise 13.3 Question 1 

Summary:

If a metallic sphere of radius 4.2 cm is melted and recast into the shape of a cylinder of radius 6 cm, the height of the cylinder is 2.744 cm.

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