Question

The diameter of a copper sphere is 18 cm. The sphere is melted and is drawn into a long wire of uniform circular cross-section. If the length of the wire is 108 m, find its diameter.

Answer 1

Answer:

The Diameter of the wire is 0.6 cm

Step-by-step explanation:

SOLUTION:

Given :  

Diameter of copper sphere =18cm

Radius of copper sphere,R = 18/2 = 9 cm  

Length of wire,h  = 108 m = 108 × 100 =  10800 cm.  

[1m = 100 cm]

Wire is in the form of cylinder

Let radius of cylindrical wire be r.  

Here, copper sphere is melted and drawn into long wire.

Therefore,  

Volume of cylindrical wire = Volume of copper sphere  

πr²h = 4/3πR³

r² × 10800 = 4/3 × 9³  

r²  = ( 4×3×9×9) / 10800  

r² = 972/10800 = 324/3600 = 9/100

r² = 9/100  

r = √9/100  

r = 3 /10 cm

r = 0.3 cm  

Diameter = 2 × radius  

Diameter = 2 × 0.3  = 0.6 cm

Hence, the Diameter of the wire is 0.6 cm

HOPE THIS ANSWER WILL HELP YOU….

Answer 2

Answer:

Diameter of wire is 0.6 cm or 6 mm

Step-by-step explanation:

Diameter of Copper Sphere = 18 cm

Radius = 9 cm [Radius = Diameter / 2]

Length of cylindrical wire = 108 m or 10800 cm [ 1 m = 100 cm]

Let radius of cylindrical wire be R

Since wire is made by melting the sphere

∴ Volume of Cylindrical wire = Volume of Copper Sphere

[Volume of Cylinder = π × Radius² × height and

Volume of Sphere = (4/3)×π×Radius³]

∴ π × R² × 10800 = (4/3) × π × (9)³

Dividing both sides by π

R² × 10800 = (4/3) × (9)³

${R^2}$ =$\frac{4\times 3\times 9\times 9}{10800}$

${R^2}$ = $\frac{9}{100}$

Taking Square Root of both sides

R = $\frac{3}{10}$

R = 0.30 cm

Radius of wire = 0.3 cm or 3 mm

[∵ Diameter = 2×Radius]

∴Diameter of wire = 0.6 cm or 6 mm

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