Advertisements
Advertisements
Question
The cross-section of a tunnel perpendicular to its length is a trapezium ABCD as shown in the following figure; also given that:
AM = BN; AB = 7 m; CD = 5 m. The height of the tunnel is 2.4 m. The tunnel is 40 m long. Calculate:
(i) The cost of painting the internal surface of the tunnel (excluding the floor) at the rate of Rs. 5 per m2 (sq. meter).
(ii) The cost of paving the floor at the rate of Rs. 18 per m2.
Advertisements
Solution
The cross-section of a tunnel is of the trapezium-shaped ABCD in which AB = 7 m, CD = 5 m and AM = BN. The height is 2.4 m and its length is 40 m.
(i) AM = BN =`( 7 - 5 )/( 2 )= ( 2 )/( 2 ) =1"m"`
∴ In ΔADM,
AD2 = AM2 + DM2 ...[ Using Pythagoras theorem ]
= 12 + (2 . 4)2
= 1 + 5.76
= `sqrt6.76`
= 2.6
AD = 2.6 m
Perimeter of the cross-section of the tunnel = ( 7 + 2.6 + 2.6 + 5 ) m = 17.2 m
Length = 40 m
∴ The internal surface area of the tunnel ( except the floor )
= ( 17.2 × 40 - 40 × 7) m2
= ( 688 - 280 ) m2
= 408 m2
Rate of painting = Rs. 5 per m2
Hence, total cost of painting = Rs. 5 × 408 = Rs. 2040
(ii) Area of floor of tunnel = l × b = 40 × 7 = 280 m2
Rate of cost of paving = Rs. 18 per m2
Total cost = 280 × 18 = Rs. 5040
APPEARS IN
RELATED QUESTIONS
The following figure shows a solid of uniform cross-section. Find the volume of the solid. All measurements are in centimeters.
Assume that all angles in the figures are right angles.
A swimming pool is 40 m long and 15 m wide. Its shallow and deep ends are 1.5 m and 3 m deep respectively. If the bottom of the pool slopes uniformly, find the amount of water in liters required to fill the pool.
A swimming pool is 18 m long and 8 m wide. Its deep and shallow ends are 2 m and 1.2 m respectively. Find the capacity of the pool, assuming that the bottom of the pool slopes uniformly.
A rectangular cardboard sheet has length 32 cm and breadth 26 cm. Squares each of side 3 cm, are cut from the corners of the sheet and the sides are folded to make a rectangular container. Find the capacity of the container formed.
The cross section of a piece of metal 2 m in length is shown. Calculate the area of cross section.
The cross section of a piece of metal 2 m in length
is shown. Calculate the volume of the piece of metal.
The figure represents the cross section of a swimming pool 10 m broad, 2 m deep at one end, 3 m deep at the other end. Calculate the volume of water it will hold when full, given that its length is 40 m.
The given figure is a cross -section of a victory stand used in sports. All measurements are in centimetres. Assume all angles in the figure are right angles. If the width of the stand is 60 cm, find The space it occupies in cm3.
A swimming pool is 50 m long and 15 m wide. Its shallow and deep ends are 1.5 m and 4.5 m respectively. If the bottom of the pool slopes uniformly, find the amount of water in kilolitres required to fill the pool (1 m3 = 1000 liters).
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 flooring at the rate of Rs.2. 5 per m2.
