Question

A copper rod of diameter 1 cm and length 8 cm is drawn into a wire of length 18 m of uniform thickness. Find the thickness of the wire.

Answer 1

Answer:

The thickness of the wire is 0.67 mm

Step-by-step explanation:

Given :  

Let r be the radius of the wire

Length of cylindrical wire , h = 18 m = 1800 cm

Diameter of copper rod, d = 1 cm

Radius of copper rod , R= (1/2) cm

Length of rod, H = 8 cm

Volume of rod = πR2H

= π x (1/2)2 x 8 cubic cm

= 2π cubic cm

Volume of cylindrical wire = πr²h

Since, the copper rod  converted into a long cylindrical wire, so volume of both are equal

Volume of cylindrical rod = Volume of cylindrical wire

πR2H = πr²h

(½)² × 8 = r² × 1800

¼ × 8 = r² × 1800

2 = r² × 1800

r² = 2/1800

r² = 1/900

r² = √(1/900)

r = (1/30) cm  

r = (1/30) × 10  

[ 1 cm = 10 mm ]

r = 1/3 mm

Diameter (thickness)  of wire = 2× r =  2(1/3) = 0.666 mm = 0.67 mm

Hence, the thickness of the wire is 0.67 mm

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Answer 2

Answer:

0.066 cm

Step-by-step explanation:

the volume of the rod is equal to that of wire so

π * 0.5² * 8 = π * r² * 1800                  note :  all values in cm

0.25 * 8 =- 1800 * r²

2 = 1800 * r²

r² = 1/900

r = 1/30

the radius of the wire is 1/30

the thickness is 2*1/30 = 1/15 cm

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