Question

a hemispherical vessel of radius 14 cm is fully filled with sand this sand is poured on a level ground .the heap of sand forms a cone shape of height 7 cm calculate the area of ground occupied by the circular base of the heap of the Sand​

Answer 1

Answer:

The area of ground occupied by the conical heap will be 2464 cm²

Step-by-step explanation:

Since the sand is poured from the hemispherical vessel, hence both the volumes will remain same,

Let the Area occupied by the conical vessel = πr² = A

volume of the hemispherical vessel = 2πr³/3

= 2/3 x 22/7 x 14 x 14 x 14

= 17248/3 cm³

Volume of the

volume of the conical heap = πr²h/3 = Ah/3

= A x 7/3

equating both the volumes we get

7A/3 = 17248/3

=> A = 2464 cm²

Hence the ground occupied by the conical heap will be 2464 cm²

Answer 2

Answer:

2464 cm²

Step-by-step explanation:

a hemispherical vessel of radius 14 cm is fully filled with sand this sand is poured on a level ground .the heap of sand forms a cone shape of height 7 cm calculate the area of ground occupied by the circular base of the heap of the Sand​

Volume of hemisphere = (2/3) π R³

π = 22/7   R = 14 cm

Sand Volume = (2/3) (22/7) (14)³ = 17248/3 cm³

Volume of Cone = (1/3)π R²H

π R² = Area of ground occupied

H = 7 cm  

Volume of cone = volume of hemisphere = Volume of sand

(1/3)π R²H = 17248/3

=> (1/3)π R²7 = 17248/3

=> π R² = 2464 cm²

area of ground occupied by the circular base of the heap of the Sand​ = 2464 cm²