The cross-section of a tunnel, perpendicular to its
length is a trapezium ABCD in which AB = 8 m,DC = 6 m and AL= BM. The height of the tunnel is 2.4 m and its length is 40 m.
Find :(i) the cost of paving the floor of the tunnel at
16 per m2
(ii) the cost of painting the internal surface of
the tunnel, excluding the floor at the rate of
* 5 per m2
Hint.(i) Area of the floor = (40 x 8) m2
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Answers
Answered by
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Answer :
AM=BN=
7
−
5
2
=
2
2
=
1
m
In
△
A
D
M
A
D
2
=
A
L
2
+
D
L
2
=>
A
D
2
=
1
2
+
2.4
2
=>
A
D
2
=
1
+
5.76
=>
A
D
2
=
√
6.76
=>
A
D
=
2.6
m
Perimeter of the cross section of the tunnel =
(
5
+
2.6
+
2.6
+
7
)
m
=
17.2
m
Length =
40
m
∴
internal area of the tunnel(except floor)
=
17.2
×
40
−
40
×
7
=
688
−
280
=
408
m
2
Rate of painting=
5
m
2
=
408
×
5
m
2
=
2040
Rs
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