Region R is revolved about the line y=1 to form a solid of revolution.


a. What is the radius of a cross section of the solid at a point x in [0, 4]?

Use the region R that is bounded by the graphs of y=1+√x,x=4, and y=1 complete the exercises.

Region R is revolved about the x-axis to form a solid of revolution whose cross sections are washers.

d. Write an integral for the volume of the solid.

Use the region R that is bounded by the graphs of y=1+√x,x=4, and y=1 complete the exercises.

Region R is revolved about the y-axis to form a solid of revolution whose cross sections are washers.

b. What is the inner radius of a cross section of the solid at a point y in [1, 3]?

Use the region R that is bounded by the graphs of y=1+√x,x=4, and y=1 complete the exercises.

Region R is revolved about the y-axis to form a solid of revolution whose cross sections are washers.

c. What is the area A(y) of a cross section of the solid at a point y in [1, 3]?

Use the region R that is bounded by the graphs of y=1+√x,x=4, and y=1 complete the exercises.

Region R is revolved about the y-axis to form a solid of revolution whose cross sections are washers.

d. Write an integral for the volume of the solid.

Region R is revolved about the line y=1 to form a solid of revolution.

c. Write an integral for the volume of the solid.

Region R is revolved about the line x=4 to form a solid of revolution.

a. What is the radius of a cross section of the solid at a point y in [1, 3]?

For the following regions R, determine which is greater—the volume of the solid generated when R is revolved about the x-axis or about the y-axis.

R is bounded by y=4−2x, the x-axis, and the y-axis.

For the following regions R, determine which is greater—the volume of the solid generated when R is revolved about the x-axis or about the y-axis.

R is bounded by y=1−x^3, the x-axis, and the y-axis.