32:51 On a coordinate plane, trapezoids A B D C and M N P Q are shown. The length of A B is 4 units and the length of B D is 2 units. The length of M N is 10 units and the length of N P is 6 units.

Is trapezoid ABDC the result of a dilation of trapezoid MNPQ by a scale factor of Two-fifths? Why or why not?

Yes, because AB and CD are each Two-fifths the lengths MN and QP.
Yes, because sides AB and CD are parallel to sides MN and QP.
No, because AB is Two-fifths the length MN but CD is One-third the length QP.
No, because sides AB and CD have different slopes from sides MN and QP.

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)