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Question
The given figure shows the cross section of a water channel consisting of a rectangle and a semi-circle. Assuming that the channel is always full, find the volume of water discharged through it in one minute if water is flowing at the rate of 20 cm per second. Give your answer in cubic metres correct to one place of decimal.
Solution
Length = 21 cm, Breadth = 7 cm
Radius of semicircle = `21/2 cm`
Area of cross section of the water channel
= `l xx b + 1/2pir^2`
= `21 xx 7 + 1/2 xx 22/7 xx 21/2 xx 21/2`
= `147 + 693/4`
= `(588 + 693)/4`
= `1281/4 cm^2`
Flow of water in one minute at the rate of 20 cm per second
`=>` Length of the water column = 20 × 60 = 1200 cm
Therefore, volume of water
= `1281/4 xx 1200 cm^3`
= 384300 cm3
= `384300/(100 xx 100 xx 100) m^3 `
= 0.3843 m3
= 0.4 m3
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