Mathematics
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 ₹ 2.25 per m2.
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Answer
Given,
Breadth of tunnel (b) = 6 m
Height of tunnel (h) = 8 m
Length of tunnel (l) = 35 m
Let radius of semi-circle be r meters.
From figure,
⇒ 2r = 6
⇒ r = 3 m.
Circumference of semi-circle = πr = m.
Internal surface area of tunnel = Circumference of semi-circle × Length + Area of side interior rectangular walls
= πrl + hl + hl
= πrl + 2hl
=
= 330 + 560
= 890 m2.
Given,
Rate of plastering = ₹ 2.25 per m2.
Total cost = 890 × ₹ 2.25 = ₹ 2002.50.
Hence, cost of plastering internal surface area of tunnel = ₹ 2002.50
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