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प्रश्न
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.
बेरीज
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उत्तर
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
\[\Rightarrow \pi r^2 l = \frac{4}{3}\pi R^3 \]
\[ \Rightarrow l = \frac{\frac{4}{3} R^3}{r^2}\]
\[ \Rightarrow l = \frac{\frac{4}{3} \times \left( 9 \right)^3}{\left( 0 . 2 \right)^2}\]
\[ \Rightarrow l = 24300 \text{ cm } \]
\[\Rightarrow l = \frac{24300}{100}\]
l = 243 m ...[∵ 1 m = 100 cm]
Thus, the length of the wire is 243 m.
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