The radius of a right circular cone and a right circular cylinder are in the ratio 3:4. If the ratio of the height of the cone and the cylinder is 2:3 ,then what is the ratio of the volume of cone to the volume of cylinder ?

For a cone, volume = (1/3)πr²h. For a cylinder, volume = πr²h. Given r_cone : r_cylinder = 3 : 4 and h_cone : h_cylinder = 2 : 3. Let r_cone = 3k, r_cylinder = 4k, h_cone = 2m, h_cylinder = 3m. Volume of cone = (1/3)π(3k)²(2m) = (1/3)π(9k²)(2m) = 6πk²m. Volume of cylinder = π(4k)²(3m) = π(16k²)(3m) = 48πk²m. Ratio V_cone : V_cylinder = 6πk²m : 48πk²m = 6 : 48 = 1 : 8.