A solid sphere of radius 'r' is melted and recast into a hollow cylinder of uniform thickness. If the external radius of the base of the cylinder is 4 cm, its height 24 cm and thickness 2 cm, find the value of 'r'.
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Answer:
The radius 'r' of a solid sphere is 6 cm.
Step-by-step explanation:
SOLUTION :
Given :
External radius of a hollow cylinder, R = 4 cm
Height of a cylinder, h = 24 cm
Thickness of a cylinder = 2 cm
Inner radius of a hollow cylinder ,r1 = External radius - Thickness
r1 = 4 - 2 = 2 cm
Inner radius of a hollow cylinder ,r1 = 2 cm
Here, solid sphere of Radius 'r' is melted and recast into a hollow cylinder.
Volume of hollow cylinder = volume of sphere
π(R² - r1²) h = 4/3 πr³
(R² - r1²) h = 4/3 × r³
(4² - 2²)× 24 = 4/3 × r³
(16 - 4) × 24 = 4/3 × r³
12 × 24 = 4/3 × r³
r³ = (12 × 24 × 3)/4
r³ = 3 × 24 × 3
r = ³√3 × 2 × 2 × 2× 3 × 3
r = ³√(3× 3 × 3 )× (2 × 2 × 2)
r = 3 × 2 = 6 cm
r = 6 cm
Hence, the radius of a solid sphere is 6 cm.
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