(Solved): please help Derive the volume formula for a right circular cone of height \( h \) and radius \( r \) ...

Derive the volume formula for a right circular cone of height \( h \) and radius \( r \) by following the steps below. (Feel free to Google "right circular cone" to see what geometric object this is.) a) Consider the isosceles triangle obtained by slicing the cone through its vertex with a plane perpendicular to the base. Place coordinate axes on the triangle with the origin at the center of the base. With this setup, find the slope of the side of the triangle in the first quadrant. (Hint: You can find the coordinates of all 3 vertices of the triangle.) b) By revolving the area in the first quadrant about the \( y \)-axis, you obtain the cone. Set up an integral using cylindrical shells that gives the volume of the cone. c) By evaluating your integral from (b), conclude that the cone has volume \( \frac{1}{3} \pi r^{2} h \).