Question

The diameter of a copper sphere is 18cm it is melted and drawn into a long wire of uniform cross section if the length of wire is 108 metre find its diameter

Answer 1

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  

Answer 2

Answer:

Step-by-step explanation:

Diameter of copper sphere =18cm

Radius of copper sphere = 18/2 = 9cm

Length of cylindrical wire = 108m or 10800cm.

Let radius of cylindrical wire be r.

Since,

Wire is made by melting the sphere.

Therefore,

Vol. Of cylindrical wire = Vol. Of copper sphere

π × r^2 × 10800 = 4/3 × π × (19)^3

On dividing both side by π

r^2 × 10800 = 4 × 3× 9× 9

r^2 = 4×3×9×9 / 10800

r^2 = 9/100

r = √9/100

r = 3 / 10

r = 0.3 cm

Diameter = 2 × radius

= 2×0.3

= 0.6

Hope it helps

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