Advertisements
Advertisements
प्रश्न
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
उत्तर
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
संबंधित प्रश्न
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 rectangular water-tank measuring 80 cm x 60 cm is filled form a pipe of cross-sectional area 1.5 cm2, the water emerging at 3.2 m/s. How long does it take to fill the tank?
The internal dimensions of a rectangular box are 12 cm x `x` cm x 9 cm. If the length of the longest rod that can be placed in this box is 17 cm; find `x`.
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 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 figure shows the cross section of 0.2 m a concrete wall to be constructed. It is 0.2 m wide at the top, 2.0 m wide at the bottom and its height is 4.0 m, and its length is 40 m. If the whole wall is to be painted, find the cost of painting it at 2.50 per sq m.
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.
ABCDE is the end view of a factory shed which is 50 m long. The roofing of the shed consists of asbestos sheets as shown in the figure. The two ends of the shed are completely closed by brick walls.
Calculate the total volume content of the shed.
