See the following image :
Let AC = 8 BC = 15 AB =17
The area of this triangle = (1/2) (8)(15) = 60
The altitude of this triangle can be found as
60 = (1/2) 17 * height
120 /17 = height = CD
This height will form the radius of two cones
The height of the smaller cone can be found as sqrt [ 8^2 - (120/17)^2 ] = 64/17 =
The height of the larger cone can be found as 17 - 64/17 = 225/17
So when triangle ACD is rotated about hypotenuse AB its volume is
(1/3) pi (120/17)^2 * (64/17) = [307200 / 4913 ] pi
And when triangle BCD is rotated about hypotenuse AB its volume id
(1/3)pi ( 120/17)^2 (225/17) = [1080000 / 4913 ] pi
So...the total volume is ( [ 307200 + 1080000] / 4913 ) pi =
[1387200 / 4913 ] pi cm^3