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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. If the whole wall is to be painted, find the cost of painting it at 2.50 per sq m.
Solution
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.
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