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Find the volume of the solid that sits above the rectangle [−1, 1]×[0, 1] in the xy-plane and below the surface z = x^(2/3)+y^(1/3)
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- Suppose that r=12 cm and h=15 cm in the right circular cylinder. Find the exact and approximate a lateral area. b total area. c volume.Find the volume of a solid bounded by y=(x2 -4) and y=(2x - x2) about the axis y=-4. What does it look like?The base of a solid sitting on the xy-plane is bounded by y = x^2 and y = 2 − x^2Find the volume of the solid if every cross section perpendicular to x-axis is square. Make sure to draw the graphs.
- Find the volume of the solid generated when the area bounded by the curve y = square root of x, y-axis, and the line y = 2 is rotated about the y-axis.Find the volume of the solid of revolution generated by revolving the region bounded by the graphs of the given equations about the given line. y = 4x − x2 and the x-axis; about the x-axis.Find the volume of the solid that is bounded above by the cylinderz = x2 and below by the region enclosed by the parabolay = 2 - x2 and the line y = x in the xy-plane.
- Find the volume of the solid whose base is the region enclosed between the curve x = 1−y² and the y-axis and whose cross sections taken perpendicular to the y-axis are squares.Find the volume of the solid generated by revolving the region bounded by x= square root (1-y^2) and the line x= 1/2 about the y-axis.A solid is formed by revolving about the y-axis, the area bounded by the curve x³=y, the y-axis and the line y=8. Find its centroid .
- The region bounded by the curves y = +-4>√x and the linesx = 1 and x = 4 is revolved about the y-axis to generate a solid. Find the volume of the solid.Find the volume of the solid generated when the region enclosed by y = root(x+3), y = root(3x+1), x=0 is revolved about the x axisThe area bounded by the line x=1 and the curve y^2-x=3 is revolved about the line y=4. Using Shell method, determine the volume of solid generated