A person is pouring coffee into a cup at rate of 3cm3/min. The bottom and the top of the cup are circles with radii (respectively) 2cm. and 5cm. The height h of the cup (the line which joins the centers of the top circle and the bottom circle) is 6cm (see center image). The two parallel radii on the top circle and the bottom circle, the line joining the centers, and the line on the side joining the end point of the considered radii make a trapezoid (see rightmost image).

What is the rate of change of the height of the coffee when the radius of poured coffee in the cup is 4cm? Hint. V = 1 3 ?h(R2 1 + R1R2 + R2 2 ) is the formula for volume of such a cup of height h, and with the top circle having radius R1 and the bottom circle having radius R2.

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