Question

A metallic sphere of radius 4.2cm is melted & recast into the shape of a cylinder of radius 6cm. Find the height of the cylinder. 2

Answer 1

Given :-

• A metallic sphere of radius 4.2cm is melted & recast into the shape of a cylinder of radius 6cm.

To find :-

• Height of cylinder

Solution :-

• Radius of metallic sphere = 4.2cm

• Radius of cylinder = 6cm

It is given that metallic sphere recast into the shape of cylinder.

→ Volume of sphere = Volume of cylinder

→ 4/3 πr³ = πr²h

Cancel " π "

→ 4/3 × r³ = r² × h

→ 4/3 × 4.2 × 4.2 × 4.2 = 6 × 6 × h

→ 4 × 1.4 × 4.2 × 4.2 = 36h

→ 5.6 × 4.2 × 4.2 = 36h

→ 5.6 × 17.64 = 36h

→ h = 5.6 × 17.64/36

→ h = 1.4 × 17.64/9

→ h = 1.4 × 1.96

→ h = 2.74cm

Hence,

• Height of cylinder is 2.74cm

Answer 2

Answer:

• Radius of Sphere ( r ) = 4.2 cm
• Radius of Cylinder ( R ) = 6 cm
• Height of Cylinder ( h ) = ?

whenever we cast one solid shape to another, Volume of metal remains unchanged.

• According to the Question :

⇒ Vol. of Cylinder = Vol. of Sphere

⇒ πR²h = 4/3 πr³

⇒ R²h = 4/3 r³

• Putting the values

⇒ (6)² × h = 4/3 × (4.2)³

⇒ 6 × 6 × h = 4/3 × 4.2 × 4.2 × 4.2

⇒ h = 4 × 1.2 × 0.7 × 0.7

⇒ h = 2.352 cm

∴ Height of Cylinder is 2.352 cm.