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प्रश्न
The internal and external diameters of a hollow hemispherical shell are 6 cm and 10 cm, respectively. It is melted and recast into a solid cone of base diameter 14 cm. Find the height of the cone so formed.
उत्तर
Internal diameter of the hemispherical shell = 6 cm
Therefore, internal radius of the hemispherical shell = 3 cm
External diameter of the hemispherical shell = 10 cm
External radius of the hemispherical shell = 5 cm
Volume of hemispherical shell `= 2/3 pi (5^3 -3^3) = 196/3xx22/7=616/3 "cm"^3`
Radius of cone = 7 cm
Let the height of the cone be h cm.
Volume of cone =` 1/3pir^2h = 1/3xx22/7xx7xx7h= (154h)/3 "cm"^3`
The volume of the hemispherical shell must be euqal to the volume of the cone therefore
`(154h)/3 = 616/3`
`rArr h = 616/154 =4 "cm"`
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