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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.
Solution
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
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