Advertisements
Advertisements
Question
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
Solution
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
RELATED QUESTIONS
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.
The cross-section of a piece of metal 4 m in length is shown below. Calculate :
(i) The area of the cross-section;
(ii) The volume of the piece of metal in cubic centimeters.
If 1 cubic centimeter of the metal weighs 6.6 g, calculate the weight of the piece of metal to the nearest kg.
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.
Find the length of 22 kg copper wire of diameter 0.8 cm, if the weight of 1 cm3 copper is 4.2 g.
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 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.
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.
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.
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.
