The diameter of the internal and external surfaces of a hollow hemispherical shell are 6 cm. and 10 cm. respectively. It is melted and recast into a solid cylinder of diameter 14 cm. Find the height of the cylinder.
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Given:
Internal diameter of hemisphere is 6cm.
External diameter of hemisphere is 10cm.
Diameter of cylinder is 14 cm.
To find:
Height of the cylinder.
Solution:
1) In the case of recast and remold the volume in both cases will remain same.
2) So here the volume of the hollow hemisphere is same as the volume of the cylinder.
- 2/3π(R₁³-R₂³) = πR²H
- 2/3(5³-3³) = 7²×H
- (2/3)×98 = 49×H
- H = 4/3
The height of the cylinder is 4/3 that is 1.33 cm.
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