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. - Geometry

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.

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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Balbharati Mathematics 2 Geometry 10th Standard SSC Maharashtra State Board
Chapter 7 Mensuration
Practice set 7.4 | Q 8 | Page 161