What is the area of cross-section of the tunnel?

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Solution

Q.
The Atal Tunnel, also known as the Rohtang Tunnel, is a highway tunnel built under the Rohtang Pass in the eastern Pir Panjal range of the Himalayas, located on the Leh–Manali highway in Himachal Pradesh. Spanning a length of 9.02 km, it is the world’s longest tunnel situated above 10,000 feet and is named after the former Prime Minister of India, Atal Bihari Vajpayee. The cross-section of a tunnel is shown in figure. The radius of circular part is $5 square root of 2 space end root m e t r e s space a n d angle A O B equals 90 degree.$

Based on the above information, answer the following questions:

(iii) (b) What is the area of cross-section of the tunnel

1 $\frac{70 π}{2} + 25 m^{2}$

2 $\frac{75 π}{2} + 25 m^{2}$

3 $\frac{75 π}{2} + 20 m^{2}$

4 $\frac{75 π}{2} + 19 m^{2}$

Ans.
(2)

Area of cross-section of the tunnel

$= \frac{270 °}{360 °} \times π r^{2} + ar △ A O B$

$= \frac{3}{4} π r^{2} + \frac{1}{2} \times O A \times O B$

$= \frac{3}{4} π (5 \sqrt{2})^{2} + \frac{1}{2} \times 5 \sqrt{2} \times 5 \sqrt{2}$

$= \frac{75 π}{2} + 25 m^{2}$

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