Mathematics
A building is in the form of a cylinder surmounted by a hemisphere valted dome and contains of air. If the internal diameter of dome is equal to the total height of the building, find the height of the building.
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Answer
The below figure shows the building in the form of a cylinder surmounted by a hemisphere valted dome:
Let the radius of the dome be r.
∴ Internal diameter = 2r.
Given, internal diameter is equal to height.
∴ Height of building (h) = 2r.
Height of hemispherical area = r.
So, height of cylindrical area, h1 = 2r - r = r.
Volume of building (V) = Volume of cylindrical area + Volume of hemispherical area.
Given, V =
h = 2r = 2(2) = 4 m.
Hence, the height of the building is 4 m.
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