the diameter of a sphere is 6cm. It is melted and drawn into a wire of diameter 4mm. Calculate the length of wire.
Answers
Answer: 900cm
Step-by-step explanation:
Diameter of the sphere = 6cm ⇒ Radius = 3cm
Volume of a sphere = 4/3(πr³)
= 4/3 × π × 3³
= 4/3 × π × 27
= 36π
∴ Volume of sphere is 36π cm³
Since the sphere is melted and cast into a wire, the volume remains the same.
Let us assume that the shape if the wire is perfectly cylindrical
Volume of cylinder = πr²h
36π = π × (0.4/2)² × h [∵ 4mm = 0.4cm; radius = diameter/2]
36 = 0.04 × h
h = 36/0.04
h = 3600/4
∴ h = 900 cm
The length of the wire is 900cm or 9m