Sum

The radius of a metallic sphere is 9 cm. It was melted to make a wire of diameter 4 mm. Find the length of the wire.

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#### Solution

Radius of the sphere, R = 9 cm

Radius of the wire, r = \[\frac{4}{2}\] = 2 mm = \[\frac{2}{10}\] = 0.2 cm (1 cm = 10 mm)

Let the length of the wire be l cm.

It is given that the metallic sphere is melted to make the wire.

∴ Volume of metal in the wire = Volume of the metallic sphere

\[\Rightarrow \pi r^2 l = \frac{4}{3}\pi R^3 \]

\[ \Rightarrow l = \frac{\frac{4}{3} R^3}{r^2}\]

\[ \Rightarrow l = \frac{\frac{4}{3} \times \left( 9 \right)^3}{\left( 0 . 2 \right)^2}\]

\[ \Rightarrow l = 24300 \text{ cm } \]

\[\Rightarrow l = \frac{24300}{100}\]

\[ \Rightarrow l = 243 m \left( 1 m = 100 cm \right)\]

Thus, the length of the wire is 243 m.

Concept: Surface Area of a Combination of Solids

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