Question

The diameter of a metallic sphere is 8cm.The sphere is melted and drawn into a wire of uniform cross-section.If the length of the wire is 75m, find its radius.​

Answer 1

$\qquad\quad\underline{\bf{\mid{\overline{\underline{\purple{\bigstar\: Answer:-}}}}}\mid}$⠀

We have

Diameter of the sphere =6cm

∴ Radius of the sphere=6/2=3cm

Volume of the sphere =4/3×π×3 3 cm 3=36πcm3 [V=4/3π3 3]

Let the radius of the cross-section of wire be r cm

It is given that the length of the cylindrical shaped wire is 36m

∴ Volume of the wire =(πr 2×3600)cm 3

[V=πr2h]

since metallic sphere is converted into cylindrical shaped wire.

Therefore,

Volume of the wire = Volume of the sphere⇒r

-r2=3636π\3600π

=1/100

⇒r= 1/10

1/10cm=1mm