Find the volume of the solid generated by revolving the region about the given line.

The region in the first quadrant bounded above by the line y = 7, below by the line y = 7x/6, and on the left by the y-axis, about the line y = 7

Question

Find the volume of the solid generated by revolving the region about the given line.

The region in the first quadrant bounded above by the line y = 7, below by the line y = 7x/6, and on the left by the y-axis, about the line y = 7

anonymous · Answer

The solid you'll obtain by revolving that region is a cone.
The volume of a cone = (1/3)*pi*(r^2)*h
where the radius (r) is the intersection between y=7 and y=(7/6)x
7=(7/6)x
x = 6

So, R = 6 and H = 7

Now solving the formula:
V = (1/3)*pi*(6^2)*7 = 263.8937829015426320308620441954782422725622295475088889618953457538565781280415558847549253287378337105004392671157137583558829472022