The vertices of a triangle are at (0,0), (8,8) and (4,12). What is the volume, in cubic units, of the figure created by rotating the triangle about y = x ?

Answer 1

triangle with vertices (0,0), (8,8) and (4,12)

rotated about the line y=x

has 2 vertices on that line, (0,0) and (8,8)'

(4,12) is off the line

and is reflected over y=x with a point (12,4) on the opposite side

a cone is created with height= 8sqr2, apex at the origin, center of the base at (8,8)

base Area = pi(4sqr2)^2 = 32pi

cone's volume = 1/3 base Area times height

= (1/3)32pi(8sqr2)

=(256pi/3)sqr2 cubic units