What is the volume if thr cone in cubic inches

  27π in³ ≈ 84.8 in³

Step-by-step explanation:

The formula for the volume of a cone is ...

  V = (1/3)πr²·h

where r represents the radius of the base of the cone, and h represents its height perpendicular to the base.

The diagram shows r = 3 in, and h = 9 in. Putting these numbers into the formula, we get ...

  V = (1/3)π·(3 in)²·(9 in) = 27π in³

The volume is 27π in³, about 84.8 cubic inches.

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'.