SOLUTION: Right triangle ABC has legs with lengths 19 and 95 units. The triangle is to be rotated in space about one of its three sides. What is the maximum possible volume of the resulting

Question 75622: Right triangle ABC has legs with lengths 19 and 95 units. The triangle is to be rotated in space about one of its three sides. What is the maximum possible volume of the resulting solid?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Right triangle ABC has legs with lengths 19 and 95 units. The triangle is to be rotated in space about one of its three sides. What is the maximum possible volume of the resulting solid?
:
When the triangle is rotated 360 degrees about one of the legs it forms a cone
The volume of a cone = 1/3*pi*r^2*h
:
When it is rotated about the shorter dimension (19), this makes the longer
dimension (95) the radius which is squared in the formula so that has to be
the greater volume which is:
V = 1/3 * pi * 95^2 * 19 = 179568.2 cu units
:
If rotated around the longer dimension:
V = 1/3 * pi * 19^2 * 95 = 35913.6 cu units
:
If you rotate it around the hypotenuse it does not form a regular cone so I don't think that would be the dimension of max volume.
:
Let me know if I am all wrong about this. ankor@dixie-net.com
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