Advertisements
Advertisements
प्रश्न
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.
उत्तर
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.
APPEARS IN
संबंधित प्रश्न
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.
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.
A school auditorium is 40 m long, 30 m broad and 12 m high. If each student requires 1.2 m2 of the floor area; find the maximum number of students that can be accommodated in this auditorium. Also, find the volume of air available in the auditorium, for each student.
A rectangular field is 112 m long and 62 m broad. A cubical tank of edge 6 m is dug at each of the four corners of the field and the earth so removed is evenly spread on the remaining field. Find the rise in level.
Find the length of 22 kg copper wire of diameter 0.8 cm, if the weight of 1 cm3 copper is 4.2 g.
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.
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 total surface area in m2.
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 flooring at the rate of Rs.2. 5 per m2.
The cross section of a swimming pool is a trapezium whose shallow and deep ends are 1 m and 3 m respectively. If the length of the pool is 50 m and its width is 1.5 m, calculate the volume of water it holds.
