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
Answers
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.
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