Question 57

A solid spherical copper ball, whose diameter is 14 cm, is melted and converted into a wire having diameter equal to 14 cm. The length of the wire is

Solution

Radius of spherical copper ball(r) = 7cm

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

Radius of Cylindrical wire(R) = 7cm

Let length of wire be 'L'

Volume of cylinder = $$\prod R^2L$$

Here Volume of sphere = Volume of sphere

$$\frac{4}{3}\prod r^3$$ = $$\prod R^2L$$

$$\frac{4}{3}\times7\times7\times7$$ = 7$$\times$$7$$\times$$L

$$\therefore$$ Length of the wire 'L' = $$\frac{28}{3}$$ cm

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