Question

The cross-section of a railway tunnel is a rectangle 6 m broad and 8 m high surmounted by a semi-circle as shown in the figure. The tunnel is 35 m long. Find the cost of plastering the internal surface of the tunnel (excluding the floor) at the rate of Rs. 2.25 per m².

Answer 1

Breadth of the tunnel = 6 m

Height of the tunnel = 8 m

Length of the tunnel = 35 m

Radius of the semi-circle = 3 m 

Circumference of the semi-circle = πr

= `22/7 xx 3`

= `66/7` m 

Internal surface area of the tunnel

= `35(8 + 8 + 66/7)` 

= `35(16 + 66/7)` 

= `35((112 + 66)/7)` 

= `35 xx 178/7` 

= 890 m² 

Rate of plastering the tunnel = Rs. 2.25 per m² 

Therefore, total expenditure = Rs. `890xx225/100`

= `890 xx 9/4`

= `8010/4`

= Rs. 2002.5