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A building is in the form of a cylinder surmounted by a hemisphere elica vaulted dome and contains 880 upon 21m3 of air if the internal diameter of dome is equal to its total height above the floor find the height of the building?
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A building is in the form of a cylinder surmounted by a hemisphere eli...
GIVEN :
Volume of air = 880/21 m^3
Internal diameter (d) = H
Internal Diameter = 2r = H
Total Height of the building (H) = 2r…(1)
Height of the building = height of the cylinder + radius of the hemispherical Dome
H = h + r
2r = h +r [from eq 1]
2r -r = h
r = h …(2)
Volume of air inside the building = Volume of cylindrical portion + Volume of hemispherical portion
πr^2h + (2πr^3 /3)= 880/21
π(h)^2h + (2π(h)^3 /3)= 880/21
[From eq 2, r= h]
πh^3 +2/3 πh^3 = 880/21
πh^3(1+2/3) = 880/21
πh^3[(3+2)/3] = 880/21
πh^3[5/3] = 880/21
22/7 * h^3 * 5/3 = 880/21
h^3 = (880 *3 *7) / 21 * 22 * 5
h^3 = 40 /5 = 8
h^3 = 8
h = 3√8 = 3√2*2*2
h = 2 m
h= r = 2 m [From eq 2, r= h]
Total height of the building( H) = 2r = 2*2 = 4 m
Hence, the Total height of the building is 4m.
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A building is in the form of a cylinder surmounted by a hemisphere elica vaulted dome and contains 880 upon 21m3 of air if the internal diameter of dome is equal to its total height above the floor find the height of the building?
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A building is in the form of a cylinder surmounted by a hemisphere elica vaulted dome and contains 880 upon 21m3 of air if the internal diameter of dome is equal to its total height above the floor find the height of the building? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about A building is in the form of a cylinder surmounted by a hemisphere elica vaulted dome and contains 880 upon 21m3 of air if the internal diameter of dome is equal to its total height above the floor find the height of the building? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A building is in the form of a cylinder surmounted by a hemisphere elica vaulted dome and contains 880 upon 21m3 of air if the internal diameter of dome is equal to its total height above the floor find the height of the building?.
A building is in the form of a cylinder surmounted by a hemisphere elica vaulted dome and contains 880 upon 21m3 of air if the internal diameter of dome is equal to its total height above the floor find the height of the building? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about A building is in the form of a cylinder surmounted by a hemisphere elica vaulted dome and contains 880 upon 21m3 of air if the internal diameter of dome is equal to its total height above the floor find the height of the building? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A building is in the form of a cylinder surmounted by a hemisphere elica vaulted dome and contains 880 upon 21m3 of air if the internal diameter of dome is equal to its total height above the floor find the height of the building?.
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