Question

The diameter of a metallic sphere is 6 cm .The sphere is melted and drawn into a wire of uniform crosssection. If the lenght of the wire is 36cm. Find its radius.

Answer 1

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Answer 2

$\mathfrak{\huge{Answer:}}$

Given diameter of the sphere = 6 cm

Radius of the sphere will be = $\sf{\frac{6}{2}}$ = 3 cm

Volume of the sphere = $\tt{\frac{4}{3} \pi r^{3}}$

Volume of the sphere = $\tt{\frac{4}{3} \pi (3^{3})}$

Volume of the sphere = $\tt{4\pi \times 9}$

Volume of the sphere = $\tt{36 \pi}$

Given length of the wire = 36 cm

Volume of the wire ( which is a cylinder ) and the Volume of the mettalic sphere will be the same, as the wire is made from the sphere and the only thing will won't change even after the change in shape is the Volume.

Thus :
Volume of wire = Volume of sphere

Volume of wire = $\tt{36 \pi}$

Volume of a cylinder = $\sf{\pi r^{2} h}$

Volume of a cylinder = $\tt{36 \pi r^{2}}$

=》 $\tt{\cancel36 \cancel\pi\ = \cancel36\cancel \pi r^{2}}$

=》 $\tt{r = 1\:cm}$

Thus, the radius of the wire is 1 cm.

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