Question

The diameter of a copper sphere is 12cm. The sphere is melted and drawn into a long wire of uniform circular cross -section. If the length of the wire is 72cm,find it's thickness

Answer 1

radius 6 cm

volume of sphere 4/3×22/7×r×r×r=2715.42

length of wire = 72 cm

volume of sphere = volume of wire

volume of wire=22\7×r×r×h=2715.42

so r=3.46 ×2 so that it is diameter=6.92 cm

Answer 2

Given :

The diameter of a copper sphere is 12cm. The sphere is melted and drawn into a long wire of uniform circular cross -section.

To Find :

If the length of the wire is 72cm,find it's thickness

Solution:

Diameter of sphere = 12 cm

Radius of sphere = $\frac{12}{2} = 6 cm$

Volume of sphere = $\frac{4}{3} \pi r^3 = \frac{4}{3} \pi (6)^3$

We are given that the sphere is melted into a long wire

So, Volume of sphere = Volume of wire

Volume of wire(cylindrical)=$\pi r^2 h = \pi r^2 (72)$

So, $\frac{4}{3} \pi (6)^3= \pi r^2 (72)\\\frac{4}{3} (6)^3= r^2 (72)\\\frac{4}{3} \times 6^3 \times \frac{1}{72}=r^2\\\sqrt{\frac{4}{3} \times 6^3 \times \frac{1}{72}}=r\\2=r$

Diameter of wire = 2r=2(2)=4 cm

Hence The thickness of wire is 4 cm