A building is in the form of a cylinder surmounted by a hemispherical dome. The base diameter of the dome is equal to of the total height of the building. Find the height of the building, if it contains m3 of air.
Let the radius of the hemispherical dome be 'r' metres and the total height of the building be 'h' metres.
Since, the base diameter of the dome is equal to of the total height, 2r =.
Let H metres be the height of the cylindrical portion.
Therefore, H= h - = metres
Volume of the air inside the building
= volume of air inside the dome+ volume of the air inside the cylinder
= cu. metres
Volume of the air inside the building is m3 = m3.
Thus, the height of the building is 6 m.
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