1. The base of a solid S is the shaded region in the xy-plane enclosed by the x-axis, the y-axis and the graph of y=1-sinx. For each x, the cross section of S perpendicular to the x-axis at the point (x,0) is an isosceles right triangle whose hypotenuse lies in the xy-plane.
(a) Find the area of the triangle as a function of x.
(b) Find the volume of S.
2. An oil storage has the shape obtained by revolving the curve y=9*x^4/625 from x=0 to x=5 about the y-axis, where x and y are measured in feet. Oil flows into the tank at the constant rate of 8 cubic feet/min.
(a) find the volume of the tank. Indicate units of measure.
(b) To the nearest minute, how long would it take to fill the tank if the tank was empty initially ?
(c) Let h be the depth ,in feet, of oil in the tank. How fast is the depth of the oil in the tank increasing when h=4 ? Indicated units of measure.