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

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



cool cool cool

CPhill  Jun 24, 2018

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