Question

Twelve solid spheres of the same size are made by melting a solid metallic cylinder of base diameter 2 cm and height 16 cm. The diameter of each sphere is ______.

Options

• 4 cm

• 3 cm

• 2 cm

• 6 cm

Answer 1

Twelve solid spheres of the same size are made by melting a solid metallic cylinder of base diameter 2 cm and height 16 cm. The diameter of each sphere is 2 cm.

Explanation:

As we know,

Volume of cylinder = πr²h

Where r = base radius

h = height of cylinder

For given solid cylinder,

Base diameter = 2 cm

Base radius, r = 1 cm  ...[As radius = `1/2` diameter]

Height, h = 16 cm

Volume of cylinder, V = π(1)²(16) = 16π cm³

Now,

Let the radius of sphere be r

Volume of sphere = `4/2 pir^3`

Where r = radius

Volume of 12 spheres of radius r = `12(4/3 pir^3) = 16 pir^3`

Now,

Volume of 12 spheres = Volume of cylinder  ...[As volume remains same, when a metal body is melted and recast into another metal body]

⇒ 16πr³ = 16π

⇒ r³ = 1

⇒ r = `root(3)1` = 1 cm

Diameter = 2r = 2 cm

Hence, diameter of each sphere is 4 cm.