# Area, Volume, and Arc Length: Solids of Revolution: Let Them Eat Cake! Quiz

*? Put your knowledge to the test. Good luck — the Stickman is counting on you!*

**Area, Volume, and Arc Length***R*be the region bounded by the

*y*-axis, the line

*y*= 9, and the graph . Which of the following integrals gives the volume of the region whose base is the region

*R*and whose slices perpendicular to the

*x*-axis are semicircles?

*R*be the region bounded by the line

*y*= 5 and the curve

*y*=

*x*

^{2}+ 1. What is the volume of the solid whose base is

*R*and whose cross-sections perpendicular to the

*y*-axis are squares?

*x*-axis?

(Write an integral for the volume, and evaluate your integral)

*y*=

*x*

^{2},

*x*= 2, and the

*x*-axis is rotated around the line

*y*= -2. Which of the following integrals gives the volume of the resulting solid, using the washer method?

*y*=

*x*is rotated around the

*x*-axis. What is the volume of the resulting solid, using the washer method?

*R*be the region bounded by the graph

*y*=

*x*

^{2}, the line

*x*= 2, and the

*x*-axis. What is the volume of the solid obtained when

*R*is rotated around the line

*x*= 0?

Use the washer method.

"Rotate the region bounded by the line *y* = *x*, the line *x* = 1, and the *x*-axis around the line *x* = 0. Use the shell method to find the volume of the resulting solid."

*R*be the region bounded by the line and the curve . Rotate the region

*R*around the

*x*-axis.

Which integral best represents the volume of the resulting solid, as found using the shell method?

*R*is rotated around the line

*y*= 1 to generate a solid. Which of the following statements is true?

*R*, the integral will be with respect to

*x*. If we use the shell method to find the volume of

*R*, the integral will be with respect to

*x*.

*R*, the integral will be with respect to

*x*. If we use the shell method to find the volume of

*R*, the integral will be with respect to

*y*.

*R*, the integral will be with respect to

*y*. If we use the shell method to find the volume of

*R*, the integral will be with respect to

*x*.

*R*, the integral will be with respect to

*y*. If we use the shell method to find the volume of

*R*, the integral will be with respect to

*y*.