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Math · Calculus
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(1) Sketch the region enclosed by the graphs of y and y 2r3 and find the volume of the solid produced when that region is revolved about the r-axis. (2) Sketch the region enclosed by y Ξ-and y r, and find the volume of the solid produced when that region is revolved about the y-axis. (3) Sketch the region in the first quadrant enclosed by y-r3 and y -r and find the volume of the solid produced when that region is revolved about the line x = 2. (4) Use an integral to find the volume of the solid with base the region enclosed by the graphs of yand y 1 and whose cross sections perpendicular to the y-axis are squares. Draw a picture! You will need to determine the formula for the area of cross-sections to apply the integral formula for volume. 25. VOLUMES (5) (Bonus question): Draw a circle of radius R centered at the origin (2 R2). Draw a vertical line r. (The number r will be positive and less than R so 0 <r<R.) Consider the region to the right of the line and inside the circle. If that region is revolved about the y-axis, bead is formed. Draw a picture! Use an integral to find the volume of the bead

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