A rectangle in the coordinate plane has vertices at (0, 0), (2, 0), (2, 5) and (0, 5).
Compare the cylinder formed when the rect-
angle is rotated around the x-axis to the cylinder
formed when the rectangle is rotated around
the y-axis.
Which of the three-dimensional figures has a
greater volume? Justify your answer. (Remem-
ber, the volume of a cylinder is given by the for-
mula: V = fr’h)
mk

For every corresponding pair of cross sections, the area of the cross section of a sphere with radius r is equal to the area of the cross section of a cylinder with radius and height 2r minus the volume of two cones, each with a radius and height of r. a cross section of the sphere is and a cross section of the cylinder minus the cones, taken parallel to the base of cylinder, is the volume of the cylinder with radius r and height 2r is and the volume of each cone with radius r and height r is 1/3 pie r^3. so the volume of the cylinder minus the two cones is therefore, the volume of the cylinder is 4/3pie r^3 by cavalieri's principle. (fill in options are: r/2- r- 2r- an annulus- a circle -1/3pier^3- 2/3pier^3- 4/3pier^3- 5/3pier^3- 2pier^3- 4pier^3)