Question

1. 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.
Metallic spheres ofradii 6 cm
inherei ofrodii​

Answer 1

$\underline{\underline{\sf{\maltese\:\:Question}}}$

• 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.

$\underline{\underline{\sf{\maltese\:\:Given}}}$

• Metallic Sphere Radius = 4.2 cm

• Metallic Sphere is melted and recast into the shape of a cylinder of radius 6 cm

$\underline{\underline{\sf{\maltese\:\:To\:Find}}}$

• Height of the cylinder

$\underline{\underline{\sf{\maltese\:\:Answer}}}$

• Height of cylinder is 2.744 cm

$\underline{\underline{\sf{\maltese\:\:Calculations}}}$

• Since Sphere is melted into a cylinder,

Volume of Sphere = Volume of Cylinder

We know :

• Volume of Sphere = 4/3 πr³

• Volume of Cylinder = πr²h

Where :

• r = radius

• h = height

Volume of Sphere = Volume of Cylinder

⇒ 4/3 πr³ = πr²h

⇒ 4/3 π(4.2)³ = π(4.2)²h

⇒ 4/3 π(4.2)³ = π(6)²h

⇒ 4/3 π(4.2)³ = 36πh

So, Now we need to solve for h :

⇒ 4 π(4.2)³/3 = 36πh

⇒ 4 × π × 74.088 /3 = 36πh

⇒ 4 × 74.088π /3 = 36πh

⇒ 296.352π /3 = 36πh

⇒ (296.352π /3)/36π = (36πh)/36π

⇒ 296.352π /(3 × 36π) = h

⇒ 296.352π /(108π) = h

⇒ 296.352/108 = h

⇒ 2.744 = h

Switch Sides

⇒ h = 2.744

∴ Height of cylinder is 2.744 cm

______________________________

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