+305 Triangle ABC is rotated completely around side BC, sweeping out a solid in space. Find the volume of the solid.
AB = 5, AC = 5, CB = 5
+23 When a triangle rotates around one of it sides, it creates a cone or a bicone.
The formula for the volume of a cone is V = 1/3 h(pi*r^2).
In this situation, the Height is 5, since the cone was rotated around BC.
We know that the triangle is equilateral, so the altitude would be 5/2 * sqrt(3).
This means that the radius is 5/2 * sqrt(3).
V = 1/3 5(pi * (5/2 * sqrt(3))^2)
V = 5/3 (pi * (25/4 * 3))
V = 5/3pi * 75/4
V = 5pi * 25/4
V = \(\frac{125\pi}{4}\)
