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hemispherical vessel of radius 14 cm is completely filled with sand. When this sand is poured on a flat ground, the pile of sand forms a cone. The height of this conical pile of sand is 7 cm. Then find how much area on the ground the base of the cone occupies.
Asked by sandeepsg9814 | 03 Mar, 2024, 10:11: PM

Let r = 14 cm be the radius of hemispherical vessel.

Volume of hemispherical vessel , Vh = (2/3) π r3

Hence quantity of sand = (2/3) π × (14)3   cm3 ....................................(1)

If cone of radius R and height h is formed after pouring the sand on ground , then volume of cone Vc is

Vc = (1/3) π R2 h

If height h of the cone is 7 cm , then we get

Vc = (7/3) π R2 .................................(2)

Base area ( π R2 ) of cone is obtained by equating (1) and (2)

(7/3) π R2 = (2/3) π × (14)3

π R2 = (2/7) × (14)3 cm2 = 784 cm2

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