A solid sphere of iron having radius 15 cm is to be melted and recast in the shape of a cylindrical pipe having internal and external radii 4 cm and 6 cm, respectively. Find the length (in m) of the pipe thus formed.
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Correct answer: D
Explanation
The correct answer is option 4 i.e 2.25.
Volume of solid sphere = (4/3) × π × r³
Volume = (4/3) × (22/7) × 15 × 15 × 15 = 14137.14 cm³
Volume of cylindrical pipe = π × (R² - r²) × h
So, cross-sectional area = π × (6² - 4²) = π × (36 - 16) = π × 20
Let length = h
Volume = (22/7) × 20 × h = (440/7) × h
14137.14 = (440/7) × h
h = (14137.14 × 7) / 440 ≈ 225.03 cm
h ≈ 2.25 m