33.no 3 do like example12 solution Water flows into a conical container al a rate of 7 cm's The radius of the container is5 cm and the height is 10 cm. How fast is the radius changing when the height of thewater is 5 cm ?4.Water is being pumped into a conical tank at the rate of 100 ft'min The height of thetank is 20 ft and its radius is 5 ft. How fast is the level rising when the height of thewater is 10 ft ?5. The height of a cone filled with water is 16 cm and the radius at the base of the cone is4 cm. If water is flowing out of the cone at the rate of 2 cm'/min, how fast is the depth ofthe liquid changing when the level is 8 cm deep ?The volume of water in a right circular cone of base radius 6 inches and height 18inches decreases at a rate of 2 in min. Find the rate at which the radius of the wateris decreasing at the instant when the radius is 3 inches.7. A water tank has the shape of an inverted circular cone with base radius 4 m andheight 10 m. The water flows out of the cone at a rate of 5 m SWhen the water is 6 m deep, find the rate at which the water level is rising.A conical tank with vertex down has a radius of 10 meter at the top and is 24 meter8.high. If water flows out of the tank at a rate of 20 m min, how fast is the depth of thewater decreasing when the water is 16 meter deep ?A. A tank of water in the shape of a cone is leaking at a constant rate of 2 m hr.The base radius of the cone is 5 m and the height of the tank is 14 m.Determine the rate at which the depth of the water in the tank is changing whenthe depth of the water is 6 m.10. Water is flowing out of a conical tank at a rate of 5 cm s '. The radius of the tank is4 cm and the height is 10 cm. If at a certain instant the height is 6 cm, how fast is thearea of the water surface changing ?Answers:dh16)14dh1612515drdr2b)3.4.%3Ddt12mdt8ndt25mdtdh9.dh5.dtdh125drdt2277.dt6.20%3D%3D2144xdtdhdt98dA%3Ddt9.10.225x3 33 ATED RATESMAT 3RELATED RATESExample 12:A conical water tank has a adius of 5 cm af the top and 20 cm bigh Wate fows to theLank at a rate of 4 cm's How lint is the radus changing at an instant when the heght ofthe water is 6 cm0- 5 cm20 cmSolution:dvdr= ?, h = 6= 4,h = 6204.4r4xr3.dvdr4mrdrdr%3DdiAPcms3/2

Question

33.no 3 do like example12 solution Water flows into a conical container al a rate of 7 cm's The radius of the container is5 cm and the height is 10 cm. How fast is the radius changing when the height of thewater is 5 cm ?4.Water is being pumped into a conical tank at the rate of 100 ft'min The height of thetank is 20 ft and its radius is 5 ft. How fast is the level rising when the height of thewater is 10 ft ?5. The height of a cone filled with water is 16 cm and the radius at the base of the cone is4 cm. If water is flowing out of the cone at the rate of 2 cm'/min, how fast is the depth ofthe liquid changing when the level is 8 cm deep ?The volume of water in a right circular cone of base radius 6 inches and height 18inches decreases at a rate of 2 in min. Find the rate at which the radius of the wateris decreasing at the instant when the radius is 3 inches.7. A water tank has the shape of an inverted circular cone with base radius 4 m andheight 10 m. The water flows out of the cone at a rate of 5 m SWhen the water is 6 m deep, find the rate at which the water level is rising.A conical tank with vertex down has a radius of 10 meter at the top and is 24 meter8.high. If water flows out of the tank at a rate of 20 m min, how fast is the depth of thewater decreasing when the water is 16 meter deep ?A. A tank of water in the shape of a cone is leaking at a constant rate of 2 m hr.The base radius of the cone is 5 m and the height of the tank is 14 m.Determine the rate at which the depth of the water in the tank is changing whenthe depth of the water is 6 m.10. Water is flowing out of a conical tank at a rate of 5 cm s '. The radius of the tank is4 cm and the height is 10 cm. If at a certain instant the height is 6 cm, how fast is thearea of the water surface changing ?Answers:dh16)14dh1612515drdr2b)3.4.%3Ddt12mdt8ndt25mdtdh9.dh5.dtdh125drdt2277.dt6.20%3D%3D2144xdtdhdt98dA%3Ddt9.10.225x3 33 ATED RATESMAT 3RELATED RATESExample 12:A conical water tank has a adius of 5 cm af the top and 20 cm bigh Wate fows to theLank at a rate of 4 cm's How lint is the radus changing at an instant when the heght ofthe water is 6 cm0- 5 cm20 cmSolution:dvdr= ?, h = 6= 4,>h = 6204.4r4xr3.dvdr4mrdrdr%3DdiAPcms3/2

Accepted Answer

We have to find rate of change of Radius.

Water flows into a conical container at a rate of 7 cm's The radius of the container is 5 cm and the height is 10 cm. How fast is the radius changing when the height of the water is 5 cm ?