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.

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3.134 cm

3.477 cm

2.744 cm

2.477 cm

answer is C.

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Detailed Solution

Concept: Solving it by simply equating the equations obtained using formula for volume of both sphere and cylinder.
Their volume must remain constant when a metallic sphere is melted and then recast into the form of a cylinder.
The sphere's volume is equal to the cylinder's.
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
So, the height of the cylinder formed will be 2.744 cm.
Hence, the correct option is 3.

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