Question

In the following figure, shows the cross-section of railway tunnel. The radius OA of the circular part is 2 m. If ∠AOB = 90°, calculate:

the area of the cross-section.

 

Answer 1

We have a cross section of a railway tunnel. `ΔOAB`is a right angled isosceles triangle, right angled at O. let OM be perpendicular to AB.

Area of cross section, 

`3/4 ("Area of circle")+"Area o"f ΔOAB`

`=(pi)(2)^2(3/4)+1/2(2)(2)`

`=(3pi+2)m^2`