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. Calculate the cross sectional area
Advertisements
उत्तर
Complete the diagram as shown:
Ler AD = x m
AB = AD + DB
= ( x +4)m
BC = `(1)/(2) xx "QC"`
= `(1)/(2) xx 2`
= 1m
DE = `(1)/(2) xx "PE"`
= `(1)/(2) xx 0.2`
= 0.1m
In ΔADE and ΔABC,
∠ADE = ∠ABC ...(90°each)
∠DAE - ∠BAC ...(Common angle)
∴ ΔADE ∼ ΔABC by AA test
∴ `"AD"/"AB" = "DE"/"BC"` ...(C.S.S.T.)
`(x)/(x + 4) = (0.1)/(1)`
`(10x)/(x + 4) = (10 xx 0.1)/(1)` ...Multiply by 10 on both sides
10x = x + 4
9x = 4
x = `(4)/(9)"m"`
∴ AB = `(4)/(9) + 4`
= `(40)/(9)"m"`
Area of the cross section of the wall
= A(ΔAQC) - A(ΔAPE)
= `(1)/(2) xx "QC" xx "AB" - (1)/(2) xx "PE" xx "AD"`
= `(1)/(2) xx 2 xx (40)/(9) - (1)/(2) xx 0.2 xx (4)/(9)`
= `(40)/(9) - (0.4)/(9)`
= `(39.6)/(9)`
= 4.4
∴ The area of the cross section of the wall is 4.4sq.m.
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 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?
Find the length of a solid cylinder of diameter 4 cm when recast into a hollow cylinder of outer diameter 10 cm, thickness 0.25 cm and length 21 cm? Give your answer correct to two decimal places.
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.
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. Calculate the volume of the concrete in the wall
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.
If the cost of asbestos sheet roofing is Rs. 20 per m2, find the cost of roofing.
A hose-pipe of cross section area 3 cm2 delivers 1800 liters of water in 10 minutes. Find the speed of water in km/h through the pipe.
