Rainflow is a new U- Shaped system of guttering. The cross section is a semi circle with a radius of x topped by an open rectangle of height h.
The total distance ABC is 20cm
For which values of x and h will rainflow carry the most water ?
volume = (area of cross-section) x length
= ( (1/2)π x^2 + 2xh)(20)
= 10πx^2 + 40xh
d(volume)/dx = 20πx + 40x dh/dx + 40h
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