The diameters of internal and external surfaces of a hollow spherical shell are 10 cm and 6 cm respectively. If it is melted and recast into a solid cylinder of length of 
, find the diameter of the cylinder.
Answers
Answer :
The diameter of the cylinder is 14 cm.
SOLUTION :
Given :
Length (h) of the solid cylinder = 2 ⅔ = 8/3 cm
Internal diameter of the hollow sphere = 6 cm
Internal radius of the hollow sphere = 6/2 cm = 3 cm
External diameter of the hollow sphere = 10 cm
External radius of the hollow sphere = 10/2 cm = 5 cm
Volume of the hollow spherical shell = 4/3π(R³ − r³)
Volume of the solid cylinder = πr²×h
Since, the hollow spherical shell is melted and recast into a solid cylinder , so volume of both are equal
4/3π(R³ − r³) = πr²×h
4/3π(5³ - 3³) = πr² × 8/3
4/3 (125 - 27) = r² × 8/3
4/3 × 98 = r² × 8/3
4 × 98 = 8r²
r² = (4 × 98)/8
r² = 98/2 = 49
r² = 49
r = √49
r =7
Radius of the cylinder = 7 cm
Diameter of the cylinder = 2 × r = 7 × 2 = 14 cm
Hence, the diameter of the cylinder is 14 cm.
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Given :
Length (h) of the solid cylinder = 2 ⅔ = 8/3 cm
Internal diameter of the hollow sphere = 6 cm
Internal radius of the hollow sphere = 6/2 cm = 3 cm
External diameter of the hollow sphere = 10 cm
External radius of the hollow sphere = 10/2 cm = 5 cm
Volume of the hollow spherical shell = 4/3π(R³ − r³)
Volume of the solid cylinder = πr²×h
Since, the hollow spherical shell is melted and recast into a solid cylinder , so volume of both are equal
4/3π(R³ − r³) = πr²×h
4/3π(5³ - 3³) = πr² × 8/3
4/3 (125 - 27) = r² × 8/3
4/3 × 98 = r² × 8/3
4 × 98 = 8r²
r² = (4 × 98)/8
r² = 98/2 = 49
r² = 49
r = √49
r =7
Radius of the cylinder = 7 cm
Diameter of the cylinder = 2 × r = 7 × 2 = 14 cm
Hence, the diameter of the cylinder is 14 cm.