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 (in cm).

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Answer 1

Radius of metallic sphere = r = 4.2 cm

Radius of cylinder = $r_1=6cm$

Let height of cylinder = h cm
A Metallic Sphere of radius 4.2 cm is melted and recast into the shape of a cylinder of radius 6 cm.

It means that volume of cylinder is equal to volume of metallic sphere.

$\Rightarrow \frac{4}{3}.\pi .r^3=\pi .(r_1{)}^2.h$

$\Rightarrow \frac{4}{3}\times 4.2\times 4.2\times 4.2=6\times 6\times h$

$\Rightarrow h=\frac{4}{3}\times \frac{4.2\times 4.2\times 4.2}{6\times 6}$

$\Rightarrow$ h = 2.8224 cm