Question

a matallic sphere of radius 4.2 cm is melted and recast into the shape of cylinder if radius 6 cm . find the height of the cylinder​

Answer 1

GIVEN :

A metallic sphere is melted and recast into the shape of a cylinder.

Radius of the cylinder = 6cm

First, we have to find the volume of the Sphere and then the height of the cylinder.

Radius of sphere = 4.2cm

We know that,

The volume of cylinder = 4/3πr³

= 4/3 × π × 4.2 × 4.2 × 4.2

= 4/3 × 22/7 × 4.2 × 4.2 × 4.2

= 4 × 22 × 1.4 × 0.6 × 4.2

= 88 × 3.528

= 310.264

The volume of Sphere = Volume of cylinder

310.264 = πr²h

310.264 = 22/7 × 6 × 6 × h

310.264 = 22/7 × 36 × h

36 × h = 310.264 × 7/22

36 × h = 98.72

h = 98.72/36

h = 2.74

Therefore, the height of the cylinder is 2.74cm.

Answer 2

Answer :-

h = 2.744 cm

Explanation :-

Volume of the sphere

= 4/3πr³

= 4/3 × π × (4.2)³

If h is height of a cylinder of radius 6cm.

Then it's volume

= π(6)² h cm³ = 36πh cm³

Since, the volume of metal in the form of sphere and cylinder remains same.

We have,

36πh = 4/3 × π × 4.2 × 4.2 ×4.2

» h = 1/36 × 4/3 × 4.2 × 4.2 × 4.2

» h = 2.744 cm

Hence, the height of the cylinder is 2.744 cm