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A solid sphere of radius 18 cm is melted down and drawn out into a long cylindrical wire of uniform thickness 8 mm. Find the length of the wire.

A. 225 m
B. 337.5 m
C. 450 m
D. 562.5 m

User Harshana
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1 Answer

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Final answer:

To find the length of the wire, equate the volume of the solid sphere to the volume of the cylindrical wire, and solve for h.

Step-by-step explanation:

To find the length of the wire, we need to calculate the volume of the solid sphere and equate it to the volume of the cylindrical wire.

The volume of the solid sphere is given by V = (4/3)πr³, where r is the radius of the sphere.

The volume of the cylindrical wire is given by V = πr²h, where r is the radius of the wire and h is the length of the wire.

By equating the two volumes, we can solve for h, which will give us the length of the wire.

Equating the volumes: (4/3)π(18cm)³ = π(0.8cm)²h

Simplifying the equation: 2,592π = 0.64πh

Dividing both sides of the equation by 0.64π: h = (2,592π) / (0.64π) = 4,050cm = 40.5m

Therefore, the length of the wire is 40.5m.

User Blegger
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