Advertisements
Advertisements
प्रश्न
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.
उत्तर
Cost for painting will depend on the total surface area which includes 5 faces (2 cross sectional, 2 lateral rectangles and 1 top face)
Area of 1 cross section = 4.4m2 ....from (a)
Area of 2 cross section
= 2 x 4.4
= 8.8m2
To find the area of the rectangles, we need to first find length of side PQ.
PQ = AQ - AP
By applying Pythagoras theorems in ΔABQ and ΔAPD
In ΔABQ,
AQ2 = AB2 + QB2
= `(90/9)^2 + 1^2`
= `(1600)/(81) + 1`
= `sqrt(1681/81)`
= `(41)/(9)`
AQ = 4.56m
In ΔAPD,
AP2 = AD2 + PD2
= `(4/9)^2 + 0.1^2`
= `(16)/(81) + 0.01`
= `sqrt(16.81/81)`
= `(4.1)/(9)`
AP = 0.46m
PQ = AQ - AP
= 4.56 - 0.46
= 4.1m
Total surface area of 5 faces
= 2 x Area of cross section + Area of 2 lateral faces + Area of top face
= 2 x 4.4 + 2 x PQ x length + 0.2 x 40
= 8.8 + 328 + 8
= 344.8m2
Cost of painting
= 344.8 x 2.50
= Rs.862
∴ The cost of painting the wall is Rs.862.
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.
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 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?
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.
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 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.
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.
The cross section of a canal is a trapezium with the base length of 3 m and the top length of 5 m. It is 2 m deep and 400 m long. Calculate the volume of water it holds.
