Question

please answer it ,.............​

Answer 1

Answer:

Step-by-step explanation:

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.