Open Drain Problem

[JJ888]

A concrete drain is to be constructed. The flat bottom of the drain is w metres long ad the curved sides are quarter circles, each with a radius of r metres.

a) Given that the total length of the flat bottom of the drain and the 2 curved sides is 6 metres, show hat w = 6-pi r


b) using part (a), show hat the cross-sectional area (A) is given by: A = 6r - (pi r^2)/2

 

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[Deleted member 4993]

A concrete drain is to be constructed. The flat bottom of the drain is w metres long ad the curved sides are quarter circles, each with a radius of r metres.

a) Given that the total length of the flat bottom of the drain and the 2 curved sides is 6 metres, show hat w = 6-pi r


b) using part (a), show hat the cross-sectional area (A) is given by: A = 6r - (pi r^2)/2

First sketch a cross-section of the drain (hat) - labeling the given variables (e.g. radius r, bottom length w).

the curved sides are quarter circles, each with a radius of r metres.

Where are the centers of of the quarter-circles?​

I think you should assume that the flat-bottom of the cross-section is tangential to the quarter circles.

Label your sketch.

Please post the sketch (or a picture of the sketch) and further work