A building is in the form of cylinder surmounted on a hemisphere dome. The base diameter of dome is equal to 2/3 of the total height of the building. Find the height of the building if it contains 1408/21 m square of the air.
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Let the height of the cylinder is h and diameter of the hemisphere is d now the total height of the structure i.e H = h + d/2.
As given in the question,
d = (2/3)H
therefore, 2/3(h + d/2) = d
on solving, h = d = 2r ---------1
now the total surface are of the building = circumference of hemisphere + circumference of cylinder = 1408/21
2πr²+(2πrh+2πr²) =1408/21
4πr²+2πrh = 1408/21
from equ /1
4πr²+4πr²=1408/21
on solving,(put π = 3.14)
r = 1.6337m
therefore height of the building is 3.26745 m
gitasadvocate:
answer is 6m as written in the answer key, but how, i need to know that
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A building is in the form of cylinder surmounted by a hemispherical dome . the base diameter of the dome is equal to 2/3of the total height of building . find the height of the building if it contain 67*1/21 cm square of air?
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