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Question 29
A solid metallic sphere of radius 8 cm is melted and drawn into a wire of uniform cross-section. If the length of the wire is 24 m, thenits radius (in mm) is:
Solution
Volume of solid metallic sphere = Volume of wire
$$\frac{4}{3} \pi r_1^3 = \pi r_2^2 h$$
$$\frac{4}{3} \times 8^3 = r_2^2 \times 2400$$
$$r_2^2 = \frac{4}{3} \times \frac{8 \times 8 \times 8}{2400}$$
$$r_2 = \frac{16}{30}$$ cm
= $$\frac{16}{3} mm = 5 \frac{1}{3}$$ mm
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