Question

A solid lead ball of radius 7 cm was melted and then drawn into a wire of diametre 0.2cm. find the length of the wire

Answer 1

hi!
here is your answer .

Solution:
Given: Radius of lead ball(r1) = 7cm.

Also, the diameter of wire = 0.2cm.

Radius of wire (r2) = 0.2/2 = 0.1cm

Let the length of wire be h.

Volume of metal used in wire
=Volume of the lead ball.

$\pi {r2}^{2} h = \frac{4}{3} \pi {r1}^{3}$


$\pi \: {(0.1)}^{2} \times h = \frac{4}{3} \pi {(7)}^{3}$


$0.01 \times h = \frac{4}{3} \times 343$


$\frac{1}{100} \times h = \frac{4}{3} \times 343$

$h = \frac{4}{3} \times 343 \times 100$

$h = \frac{4}{3} \times 34300$

$h = 4 \times 11433.34$


$h = 45733.36cm$

$h = 457.34m$


Therefore,
The length of the wire is 457.34m.

hope this helps " !!!#