Question

ีfind the volume of a cone using calculus
no values given, use variable.​

Answer 1

Answer:

Consider the cone as a development of right angle triangle rotating around one of its leg for 360 deg creating a volume.The volume of the cone= area of the triangle × angle swept× distance of cg of the triangle from the axis of rotation.Now area of the triangle=[math]\frac{1}{2}[/math] ×leg of the triangle (base)×other leg(height of the cone)[math]=\frac{1}{2} ×r×h[/math]Angle swept =[math]2\pi[/math]CG of the triangle from axis of rotation =[math]\frac{1}{3}r[/math]So, volume of the cone[math]=\frac{1}{2} ×r×h×2\pi×\frac{1}{3}r[/math][math]=\frac{1}{3}\pi×r^2h[/math]