An xyz-coordinate system has an x-axis, a y-axis, and a vertical positive z-axis. A right circular cone labeled z = 26 - √( x² + y²) has a circular base in the xy-plane that is a circle centered at (0, 0, 0) and a vertex on the positive z-axis.
Find the volume of the solid bounded by the surface z = f(x, y) and the xy-plane.
(Type an exact answer, using pi as needed.)

V = 5858.66π

Step-by-step explanation:

This problem can be solved by using the washer method in the integration.

If you assume that the lateral of the cone is given by a line equation of the form:

r: radius of the cone = 26 (because for z=0 -> √( x² + y²)  = 26 = r)

h: height of the cone = 26 (because for x=0 and y=0, z = 26)

you can integrate in the following form to get the volume of the cone:

hence, the volume of the cone is 5858.66π

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