The diameter of a metallic sphere is 6 cm The sphere is melted and drawn into a wire of uniform circ...........

Quantitative Aptitude (CDS) Mensuration 3D

The diameter of a metallic sphere is 6 cm. The sphere is melted and drawn into a wire of uniform circular cross-section. If the length of the wire is 36m, then what is its radius equal to?

0.1 cm

0.01 cm

0.0001 cm

1.0 cm

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Explanation:

Diameter of a sphere, d = 6 cm
∴ Radius of a sphere, r =d/2= 6/2=3 cm
Let the radius of wire be R cm.
Also, given the length of wire, H = 36 m = 3600 cm
According to question, Volume of sphere = Volume of wire
⇒4/3x πr³ = π r²H
⇒4/3π(3)³ = R²×36000
⇒ R² =4×32/3600=(6)²
∴ R = 0.1 cm