Question

A solid lead ball of radius 7cm is melted and drawn into a wire of diameter 2 mm.
Find the length of the wire.

Answer 1

Answer:

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}πr2

2

h=

3

4

πr1

3

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

2

×h=

3

4

π(7)

3

0.01 \times h = \frac{4}{3} \times 3430.01×h=

3

4

×343

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

100

1

×h=

3

4

×343

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

3

4

×343×100

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

3

4

×34300

h = 4 \times 11433.34h=4×11433.34

h = 45733.36cmh=45733.36cm

h = 457.34mh=457.34m

Therefore,

The length of the wire is 457.34m.

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