Math, asked by vchandra1488, 1 year ago

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


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Answers

Answered by poonambhatt213
4

Answer:

2,464 cm^2

Step-by-step explanation:

Radius of the hemisphere vessel =14 cm

height of cone = 7 cm

hemisphere vessel converted into cone then volumes are equal

2/3πr^3 = 1/3πr^2h

2/3 x π x 14 x 14 x 14 = 1/3 x π x r^2 x 7

r^2 = 2 x 2 x 14 x 14

r = 2 x 14

∴ r= 28 cm

base of the heap of the Sand is circular so,

area = πr^2

         = 22/7 x 28 x 28

         = 22 x 28 x 4

         = 2,464 cm^2

Thus, the area of ground occupied by the circular base of the heap of the Sand is 2,464 cm^2.

Answered by amitnrw
0

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

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