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The diameter of a metallic sphere is 6 cm. The sphere is melted and drawn into a wire of uniform cross section. If the length of the wire is 36 m, find its radius.

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1 mm

2 mm

3 mm

4 mm

answer is A.

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Detailed Solution

Given,
Sphere diameter is 6 cm.
Then,
Sphere radius

r = \frac{6}{2} = 3 cm

We have,
Sphere volume

= \frac{4}{3} \times π \times r^{3} {cm}^{3}

= \frac{4}{3} \times π \times 3^{3} {cm}^{3}

= 36 π {cm}^{3}

Given, the length wire, h = 36 m
h = 3600 cm (Since 1 m = 100 cm)
Here,
Wire volume V=

π r^{2} h

V = (π r^{2} \times 3600)

As, volume remain same after recasting. Thus,
Sphere volume = Wire volume

(π r^{2} \times 3600) = 36 π

r^{2} = \frac{36 π}{3600 π}

r^{2} = \frac{1}{100}

r = \frac{1}{10} cm

r = 1 mm

(since, 1 cm = 10 mm)
So, the radius of wire is 1 mm.
Thus, the correct option is 1.

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