Volumes of Solids with Known Cross-Sections Exercises

Example 1

Let R be the region enclosed by the x-axis, the graph y = x2, and the line x = 4. Write an integral expression for the volume of the solid whose base is R and whose slices perpendicular to the x-axis are semi-circles.

Example 2

Let R be the region enclosed by the x-axis, the graph y = x2, and the line x = 4. Write an integral expression for the volume of the solid whose base is R and whose slices perpendicular to the y-axis are squares.

Example 3

Let R be the region enclosed by the x-axis, the graph y = x2, and the line x = 4. Write an integral expression for the volume of the solid whose base is R and whose slices perpendicular to the y-axis are equilateral triangles.

Example 4

Let R be the region bounded by y = x and y = x2. Write an integral expression for the volume of the solid with base R whose slices perpendicular to the y-axis are semi-circles.

Example 5

Let R be the region bounded by y = x and y = x2. Write an integral expression for the volume of the solid with base R whose slices perpendicular to the y-axis are squares

Example 6

Let R be the region bounded by y = x and y = x2. Write an integral expression for the volume of the solid with base R whose slices perpendicular to the x-axis are equilateral triangles

Example 7

Let R be the region bounded by x2 + y2 = 1. Write an integral expression for the volume of the solid with base R whose slices perpendicular to the y-axis are semi-circles.

Example 8

Let R be the region bounded by x2 + y2 = 1. Write an integral expression for the volume of the solid with base R whose slices perpendicular to the x-axis are equilateral triangles.

Example 9

Let R be the region bounded by x2 + y2 = 1. Write an integral expression for the volume of the solid with base R whose slices perpendicular to the x-axis are squares.