A building is in the form of cylinder surmountedd by a hemispherical dome and which contains 41 19/21 m cube of air. If the internal diameter of the dome is equal to its total height above the floor. Find the height of the building
Answers
hey here is your answer:-
Let r be the radius of hemisphere & Cylinder and h be the height of the Cylinder, H be the height of the Total building.
GIVEN :
Volume of air = 880/21 m³
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
πr²h + (2πr³/3)= 880/21
π(h)²h + (2π(h)³/3)= 880/21
[From eq 2, r= h]
πh³ + ⅔ πh³ = 880/21
πh³(1+⅔) = 880/21
πh³[(3+2)/3] = 880/21
πh³[5/3] = 880/21
22/7 × h³ × 5/3 = 880/21
h³ = (880 ×3 ×7) / 21 × 22 × 5
h³ = 40 /5 = 8
h³ = 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.
HOPE THIS WILL HELP YOU….
Answer:
Height is 4 m
Step-by-step explanation:
Plz mark as brainliest
