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Question
In the following diagram a rectangular platform with a semi-circular end on one side is 22 metres long from one end to the other end. If the length of the half circumference is 11 metres, find the cost of constructing the platform, 1.5 metres high at the rate of Rs. 4 per cubic metres.
Solution
Length of the platform = 22 m
Circumference of semicircle = 11 m
∴ Radius = `(c xx 2)/(2 xx pi)`
= `(11 xx 7)/22`
= `7/2 m`
Therefore, breadth of the rectangular part = `7/2 xx 2 = 7 m`
And length = `22 - 7/2`
= `37/2`
= 18.5 m
Now area of platform = `l xx b + 1/2pir^2`
= `18.5 xx 7 + 1/2 xx 22/7 xx 7/2 xx 7/2 m^2`
= `129.5 + 77/4 m^2`
= 148.75 m2
Height of the platform = 1.5 m
∴ Volume = 148.75 × 1.5 = 223.125 m3
Rate of construction = Rs. 4 per m3
Total expenditure = Rs. 4 × 223.125 = Rs. 892.50
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