Question

A metallic sphere of radius 3.6 m is melted and a wire of diameter 0.4 cm of uniform cross

section is drawn from it. Fins the length of wire.​

Answer 1

Given:

A metallic sphere of radius 3.6 m is melted and a wire of diameter 0.4 cm of uniform cross -section is drawn from it

To find:

The length of wire

Solution:

For the metallic sphere:

Radius = 3.6 m = 360 cm

∴ The volume of the metallic sphere = $\frac{4}{3} \pi r^3 = \frac{4}{3} \times \frac{22}{7} \times 360^3$

For the wire:

Diameter = 0.4 cm

So, Radius = $\frac{0.4}{2} = 0.2 \:cm$

Let's assume "h" as the length of the wire.

∴ The volume of the cylindrical wire = $\pi r^2 h = \frac{22}{7} \times 0.2^2 \times h$

Since the metallic sphere is melted into a wire, so we can say that

Volume of metallic sphere = Volume of wire

⇒ $\frac{4}{3} \times \frac{22}{7} \times 360^3 = \frac{22}{7} \times 0.2^2 \times h$

⇒ $\frac{4}{3} \times 360^3 = 0.2^2 \times h$

⇒ $h = \frac{4}{3 \times 0.2^2} \times 360^3$

⇒ $h = 1555200000\:cm$

⇒ $h = 15552\times 10^5\:cm$

Thus, the length of the wire is → $\underline{\bold{ 15552\times 10^5\:cm}}$.

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