Question

The adjoining figure shows the cross-section of a railway tunnel. The radius of the tunnel is 3.5m(i.e, OA=3.5m) and
Calculate:1. height of tunnel
2.perimeter of cross-section, including base
3. area of cross-section
4.internal surface area of the tunnel, excluding base, if the lenght is 50m.

Answer 1

Answer:

Step-by-step explanation:

height of the tunnel = OM + OC

OM perpendicular at O.

OA = OB = 3.5 m

Δ AOM is isosceles. OM = AM = h

h = OA/ √2 = 2.47 m (where OA = 3.5m )

Height of Tunnel = 2.47 + 3.5 = 5.97 m

∠AOB = 90°

Perimeter of circular part = = 3/4 of Full circular cross section

Perimeter of circular part = 3/4 x 2 Pi x 3.5 = 16.49 m

Base = 2 x h = 2 x 2.47 = 5.94 m

Perimeter of cross section + base = 5.94 + 16.49 = 22.43 m

area of cross section = Area of circular portion + Area of Δ = 3/4 x pi x 3.5 x 3.5 + 1/2 x 3.5 x 3.5

area of cross section = 35 sq. m

surface area = (3/4) × 2π × 3.5 × 50 ≈ 825 m²

surface area = 825 m²