The diameters of the internal and external surfaces of a hollow spherical shell are 6 cm and 10 cm respectively. If it is melted and recast into a solid cylinder of diameter 14 cm. find the height of the cylinder.
Answers
Answer:
The Height of the cylinder is 8/3 cm.
Step-by-step explanation:
Given :
Internal diameter of a hollow spherical shell =6 cm
Internal radius of a hollow spherical shell ,r = 3 cm
External diameter of a hollow spherical shell = 10 cm
External radius of a hollow spherical shell ,R = 5 cm
Diameter of a cylinder = 14 cm
Radius of the cylinder, r1 = 14/2 = 7 cm
Volume of the hollow spherical shell = 4/3π(R³ − r³)
Volume of the solid cylinder = πr1²×h
Since, the hollow spherical shell is melted and recast into a solid cylinder , so volume of both are equal
Volume of the hollow spherical shell = Volume of the solid cylinder
4/3π(R³ − r³) = πr²×h
4/3π(5³ - 3³) = π(7)² × h
4/3 (125 - 27) = 49 h
4/3 × 98 = 49 h
h = (4/3 × 98)/49
h = (4 × 98)/ 3 × 49
h = 8/3
Height of the cylinder = 8/3 cm
Hence, the Height of the cylinder is 8/3 cm.
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Answer:
Volume of sphere = V
s
=
3
4
π(R
e
3
−R
i
3
)
V
s
=π×7
2
×h
⇒h=
3×7
2
4(5
3
−3
3
)
=
3
8
cm