What is the volume of the geometric solid produced by the equilateral triangle in the figure below when it is rotated 360o about the altitude m?
(a) ¶m3/9
(b) ¶m2/9
(c) ¶m3/4
(d) ¶m3
(e) m3/9
Answer:
The solid produced by the triangle rotation will be a cone with a radius equal to half the side of the triangle.
We apply Pythagoras Theorem in one of the 2 right triangles created by the altitude m:
r2 + m2 = (2r)2
r = m/√3
The volume of the cone:
Vcone = ¶m(m/√3)2/3
Vcone = ¶m3/9