# Area, Volume, and Arc Length

# Volumes of Solids with Known Cross-Sections Exercises

### Example 1

Let *R* be the region enclosed by the *x*-axis, the graph *y* = *x*^{2}, 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* = *x*^{2}, 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* = *x*^{2}, 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* = *x*^{2}. 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* = *x*^{2}. 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* = *x*^{2}. 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 *x*^{2} + *y*^{2} = 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 *x*^{2} + *y*^{2} = 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 *x*^{2} + *y*^{2} = 1. Write an integral expression for the volume of the solid with base *R*

whose slices perpendicular to the *x*-axis are squares