5. Find the volume of a cone formed from a sector with a diameter of 72 7n inches and a central angle of ? . 6. The lateral edge of a regular hexagonal pyramid is two times the length of the base edge. If the apothem of the base is 8 cm, find the altitude and the volume of a cone inscribed in the pyramid. 7. If the diameter of the base remains constant, by what factor should the altitude be multiplied to produce a cone with twice volume as the original? 8. If the altitude of a cone remains constant, by what factor should the diameter be multiplied in order to construct a cone with a volume that is triple the original? 9. Water is flowing out of a conical funnel through its apex at a rate of 12 cubic inches per minute. If the funnel is initially full, how long will it take for it to be one-third full? What is the height of the water level? Assume the radius to be 6 inches and the altitude of the cone to be 15 inches. 81H 10.Two similar cones have T in.3 and 12H in.3 and the slant height of the bigger cone is 7.5 in. Find the integer solution to the height of the smaller cone. 11.lf the slant height of the cone is 16 inches and the total area is 121': square inches, find the height of the cone. 12.What is the height of a right circular cone having a slant height of 61/10 units and base radius of 6 units? 13.Find the ratio of the slant height to the radius of a right circular cone in which the volume and lateral area are numerically equal. Assume the :l'l'i'l'l Irln n'F fhn rnnn 'l'n hp 0 IInH'c