A circular hall (big room) has a hemispherical roof.The greatest height is equal to the inner diameter. Find the area of the floor, given that the capacity of the hall is
48510m^3.
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Let the greatest height = H meters
radius of the hemispherical roof = radius of the circular hall = H/2 meters
Height of cylindrical portion = H - H/2 meters = H/2 meters
Volume = π (H/2)² H/2 + 2/3 π (H/2)³ = 48510 m³
22/7 H³ (1/8 + 1/12) = 48510 m³
H = 42 m
Radius of floor/circular hall = 21 m
Area of the floor = 22/7 21² m² = 1386 m²
radius of the hemispherical roof = radius of the circular hall = H/2 meters
Height of cylindrical portion = H - H/2 meters = H/2 meters
Volume = π (H/2)² H/2 + 2/3 π (H/2)³ = 48510 m³
22/7 H³ (1/8 + 1/12) = 48510 m³
H = 42 m
Radius of floor/circular hall = 21 m
Area of the floor = 22/7 21² m² = 1386 m²
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