Right triangle ABC has legs measuring 8 cm and 15 cm. The triangle is rotated about its hypotenuse. What is the number of cubic centimeters in the volume of the resulting solid? Express your answer in terms of π.
+128407 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
