The diameter of a metallic solid sphere is 9 cm. It is melted and drawn into a wire having diameter of cross-section as 0.2 cm. Find the length of the wire
Answers
Answer:
The length of the wire is 121.5 m.
Step-by-step explanation:
Given that:
The diameter of a metallic solid sphere is 9 cm.
It is melted and drawn into a wire having diameter of cross-section as 0.2 cm.
To Find:
The length of the wire.
Concept:
If metallic solid sphere is melted and drawn into a wire then we can say that the volume of metallic solid sphere is equal to the volume of wire formed.
We have:
Radius of sphere = 9/2 = 4.5 cm
Radius of wire formed = 0.2/2 = 0.1 cm
Let us assume:
The length of the wire be h.
Formula used:
Volume of sphere = (4πr³)/3
Volume of cylinder = πR²h
Where,
r = Radius of metallic solid sphere
R = Radius of the wire formed
h = The length of the wire
Finding the length of the wire:
Volume of a metallic solid sphere = Volume of Wire
Putting the values in formula.
⇒ (4 × π × (4.5)³)/3 = π × (0.1)² × h
Cancelling π both sides.
⇒ (4 × 4.5 × 4.5 × 4.5)/3 = 0.1 × 0.1 × h
Cross multiplication.
⇒ 0.1 × 0.1 × h × 3 = 4 × 4.5 × 4.5 × 4.5
⇒ 0.03h = 364.5
⇒ h = 364.5/0.03
⇒ h = 12150
∴ The length of the wire = 12150 cm
Converting the length of the wire in m:
1 cm = 1/100 m
12150 cm = 12150/100 m
12150 cm = 121.5 m
Answer:
Solution:-
Finding the length of the wire:
- Volume of solid sphere = Volume of Wire
Putting the values in formula.
⇒ (4 × π × (4.5)³)/3 = π × (0.1)² × h
⇒ (4 × 4.5 × 4.5 × 4.5)/3 = 0.1 × 0.1 × h
⇒ 0.1 × 0.1 × h × 3 = 4 × 4.5 × 4.5 × 4.5
⇒ 0.03h = 364.5
⇒ h = 364.5/0.03
⇒ h = 12150
∴ The length of the wire = 12150 cm
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