A building is in the form of a cylinder surmounted by a hemispherical dome as shown in the figure. The base diameter of the dome is equal to 2by3 of the total height of the building . find the height of the building , if it contains 1408 by21 meter cube of air.
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Answer:
The height of the building is 6 cm
Step-by-step explanation:
Let the radius of the cylinder = radius of the hemisphere = r
Let the height of the cylinder = h
Total height of the structure = h + r
From the given condition,
d = 2(h+r)/3
=> 2r = 2(h+r)/3
=> r = (h+r)/3
=> 3r = h+r
=> h = 2r
Total volume of the air
= volume of cylinder + volume of dome = 67 1/21 = 1408/21
=> πr²h + 2πr³/3 = 1408/21
=> πr²(2r) + 2πr³/3 = 1408/21
=> 8πr³/3 = 1408/21
=> r³ = (1408 x 3 x 7)/(8 x 22 x 21)
=> r³ = 8
=> r = 2 cm
=> h = 2r = 4
Hence height of the building = h + r = 4 + 2 = 6 cm
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