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

Confusedperson
Jun 24, 2018

#1**+1 **

The triangle formed will be an 8 -15 -17 "Pythagorean Triple" right triangle

If rotated about the shorter leg....a cone with a height of 8 and a radius of 15 is formed....and its volume will be = pi ( 15)^2 * 8 / 3 = 600 pi units^3

If rotated about the longer leg....a cone with a height of 15 and a radius of 8 is fromed....and it volume will be = pi (8)^2 * 15 / 3 = 320 pi units^3

So.....rotating the triangle about the shorter leg produces the max volume of 600 pi units^3

CPhill
Jun 24, 2018