The diameter of a sphere is 42 cm.

Question:

The diameter of a sphere is 42 cm. It is melted and drawn into a cylindrical wire of diameter 2.8 cm. Find the length of the wire.

Solution:

Radius of the sphere $=\frac{42}{2}=21 \mathrm{~cm}$

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

$=\left(\frac{4}{3} \pi \times 21 \times 21 \times 21\right) \mathrm{cm}^{3}$

Radius of the wire $=\frac{2.8}{2}=1.4 \mathrm{~cm}$

Let the length of the wire be $\mathrm{h} \mathrm{cm}$. Then,

Volume of the wire $=\pi r^{2} h$

$=\left(\pi \times \frac{14}{10} \times \frac{14}{10} \times h\right) \mathrm{cm}^{3}$

Therefore,

$\frac{4}{3} \pi \times 21 \times 21 \times 21=\pi \times \frac{14}{10} \times \frac{14}{10} \times h$

$\Rightarrow 12348=\frac{49}{25} \times h$

$\Rightarrow h=\left(\frac{12348 \times 25}{49}\right)$

$\Rightarrow h=6300 \mathrm{~cm}$

$\Rightarrow h=\left(\frac{6300}{100}\right) \mathrm{m}$

 

$\Rightarrow h=63 \mathrm{~m}$

Hence, the length of the wire is 63 m.

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Ritesh shraff
March 11, 2023, 7:29 p.m.
12. A sphere of radius 42 cm is melted and recast into a cuboid wh dimensions are in the ratio 49 * 44 - 18 Find the actual dimensions of th cuboid
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