The radius of a solid sphere of some metal is 3 cm. How long a wire of…
2023
The radius of a solid sphere of some metal is 3 cm. How long a wire of diameter 4 mm can be drawn from it?
Answer: B. 9 m — CONCEPTWhen a solid is reshaped without loss of material, its volume remains unchanged. For a sphere, V = (4/3)πR3. For a cylindrical wire, V = πr2L, where L…
- A.
8·8 m
- B.
9 m
- C.
9·1 m
- D.
More than one of the above
- E.
None of the above
Show answer & explanation
Correct answer: B
CONCEPT
When a solid is reshaped without loss of material, its volume remains unchanged.
For a sphere, V = (4/3)πR3. For a cylindrical wire, V = πr2L, where L is the wire length.
APPLICATION
Convert the wire diameter: 4 mm = 0.4 cm, so its radius is r = 0.2 cm.
Find the sphere volume: V = (4/3)π(3 cm)3 = 36π cm3.
Equate the wire volume to the sphere volume: π(0.2 cm)2L = 36π cm3.
Solve: 0.04L = 36, so L = 900 cm = 9 m.
CROSS-CHECK
A 9 m wire is 900 cm long, and π(0.2 cm)2(900 cm) = 36π cm3, exactly the original sphere volume.
Therefore, the wire length is 9 m.