Question

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

Answer 1

Radius of the sphere, R = 3cm
Volume of the sphere `= ((4)/(3) pi R^(3)) cm^(3)`
`= ((4)/(3) pi xx 3 xx 3 xx 3) cm^(3) = (36pi) cm^(3)`
Let the radius of the wire formed be r cm
Then, volume of the wire `= (pi r^(2) xx h) cm^(3) = (pi r^(2) xx 36) cm^(3)`
`:. 36pi r^(2) = 36 pi rArr r^(2) = 1 rArr r = 1`
hence, radius of the wire is 1 cm