If the height of a cone is tripled and radius is held constant, then the volume will double
+130516 If the height is tripled and the radius is unchanged, the volume will triple.
To see this.....note that a cross-section of the cone will form a triangle. And triangles on the same bases are to each other as their heights. So, the triangle cross-section of the cone with its height tripled will have 3 times the area of the cone without its height tripled. And the sum of all these cross sections will form a volume three times of that of the sum of all the cross-sections of the cone with the "normal" height.
+130516 If the height is tripled and the radius is unchanged, the volume will triple.
To see this.....note that a cross-section of the cone will form a triangle. And triangles on the same bases are to each other as their heights. So, the triangle cross-section of the cone with its height tripled will have 3 times the area of the cone without its height tripled. And the sum of all these cross sections will form a volume three times of that of the sum of all the cross-sections of the cone with the "normal" height.
