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Question
The cross section of a tunnel perpendicular to its length is a trapezium ABCD as shown in the figure. AM = BN; AB = 4.4 m, CD = 3 m The height of a tunnel is 2.4 m. The tunnel is 5.4 m long. Calculate the cost of painting the internal surface of the tunnel (excluding the floor) at the rate of Rs. 5 per m2.
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Solution
The internal surface area will consist of faces formed by 1 side as length and other sides as AD, CD and BC.
AM = `(1)/(2)("AB" - "CD")`
= `(1)/(2)(4.4 -3)`
AM = 0.7
In ΔAMD, by Pythagoras theorem,
AD2 = AM2 + DM2
AD2 = (0.7)2 + (2.4)2
AD = 2.5m
AD = BC = 2.5n
Total surface area
= (length x AD) + (length x CD) + (length x BC)
= 5.4(AD + CD + BC)
= 5.4(2.5 + 3 + 2.5)
= 43.2m2
Cost of painting
= 43.2 x 5
= Rs,216
∴ The cost of painting the internal surface is Rs.216.
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