The base of a solid in the xy-plane is a circle with a radius of 3. cross sections of the solid perpendicular to the x-axis are squares. set up the integral to arrive at the volume of the solid and solve.

Step-by-step explanation:

1. Set up the integral.

The equation for the circle is

x² + y² = 9

The bottom corners of the square are at  

The length (a) of a side is

and the area (A) of the square cross-section is

A = a² = 4(9 - x²)

The volume (V) of the solid is

2. Solve the integral

for the friend request.

when a figure, such as triangle (xyz) is reflected over the line y = x to create x'y'z' the x-coordinates and y-coordinates of the original image (pre-image) will be reversed for the image. (e.g., (x, y) > (y, x)) this means that the pre-image position of the x- and y-coordinates switch places which in turn provides a mirror like image of the original xyz.  

i notice that when i draw a line segment from x to x', that the points are parallel from each other -- they are exactly across from each other and do not intersect with any other points.  

yes, think i would see the same characteristic if you drew the line segment connecting y with the reflecting line and then y' with the reflecting line because of the essence of reflections. because it is a mirror image, each point was effected the same way which leads me to conclude that they same would apply to y and y'.