CBSE Class 10 Answered

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

Volume of hemispherical vessel , V_h = (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 V_c is

V_c = (1/3) π R² h

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

V_c = (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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