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:

(i) the height of the tunnel

(ii) the perimeter of the cross-section

(iii) the area of the cross-section.



figure

Answer 1

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

(i) We have to find the height of the tunnel. We have,

Use Pythagoras theorem into get,

Let the height of the tunnel be h. So,

Thus,

Therefore,

$h=\left(2+\sqrt{2}\right)\mathrm{m}$

(ii)

Perimeter of cross-section is,

$=\left(3\mathrm{\pi }+2\sqrt{2}\right)m$

(iii)

$\left(3\mathrm{\pi }+2\right)m^2$