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.​

Answer 1

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Answer 2

Given :-

Radius of the metallic sphere = 4.2 cm

Radius of cylinder = 6 cm

To Find :-

The height of the cylinder.​

Analysis :-

Volume of Sphere = Volume of Cylinder

If a solid is recast in any other solid the volume remains the same.

Solution :-

We know that,

• r = Radius
• h = Height

Let the height of cylinder be 'h'

It is given that the sphere is melted into a cylinder.

Also given,

Radius of sphere = 4.2 cm

Radius of cylinder = 6 cm

Volume of Sphere = Volume of Cylinder

$\underline{\boxed{\sf \dfrac{4}{3} \pi r^{3}=\pi r^{2}h}}$

Substituting them,

$\sf \dfrac{4}{3} \pi \times (4.2)^{3} = \pi (6)^{2} h$

$\sf h=\dfrac{4}{3} \times \dfrac{4.2 \times 4.2 \times 4.2}{36}$

$\sf h=(1.4)^{3} =2.74 \ cm$

Therefore, the height of the cylinder is 2.74 cm