A building is in the form of a cylinder surmounted by a hemispherical dome. The base diameter of the dome is ⅔ of the total height of the building. Find the height of the building if it contains 67 ¹⁄₂₁ m² of air.
Answers
Answered by
6
Answer:
Height of building = height of cylinder + height of hemisphere
H=h+r
r is radius of cylinder and dome
diameter of dome =2/3× height of building
∴2r=
3
2
×(h+r)
∴6r=2h+2r ∴3r=h+r
∴h=2r
Volume of air in building = Volume of cylinder+ Volume of dome
∴67
21
1
=πr
2
h+
3
2
πr
3
∴
21
1408
=πr
2
(h+
3
2
r)
=πr
2
(2r+2/3r)
=πr
2
(
3
8
r)
∴
21
1408
=
3
8
πr
3
∴
7
1408
=8×
7
22
×r
3
∴r
3
=
22×8
1408
=8
∴r=2 m⇒h=4 m
Height of building =r+h=6 m
Answered by
3
Answer:
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