31. no 7 do like example 8 solution times the radius.Water is poured into a cylindrical tank whose height iswhen the radius is 3m ?times32.Iron ore pouring from a chute forms a conical pile whose height isits radius. If the radius is 200 cm and the volume changes at a rate of10000 cm's, find the rate of change of the radius.Sand is falling into a conical pile so that the radius of tha base of the pile is always e3.to half of its height. If the sand is falling al the rate of 10 cm /sec, how fast is heightthe pile increasing when the pile is 5 cm deep?4. Sand falls from an overhead bin and accumulates in a conical pile with a radius that isalways three times its height. Suppose the height of the pile increases at a rate of2 cm/s when the height of the pile is 12 cm. At what rate is the sand leaving the bin atthat instant?Sand pouring from a container forms a conical pile whose height is equal to thediameter. If the height increases at a constant rate of 5 cm/s, find the rate of change involume of sand when the pile is 10 cm high.6.An ice cube in the shape of a cube is melting at a constant rate of 4 cm/sec.Find the rate of change of the surface area of the cube when the volume is 8 cm.A block of ice in the shape of a cube is melting in such a way that the length of each ofits edges is decreasing at the rate of 2 cm/hr.At what rate is its surface area decreasing at the time its volume is 64 cm ?Assume that the block of ice maintains its cubical shape. Example 8:A spherical balloon is being inflated at a rato of B cm'sCnd the rate of change of the surface area when the radius is 10 cm.Solution.dAAP8.=7,r= 10dt4.drA =4xrdA8ar%3DdrdAAPdvdAdtdAAPdrdVdtdr18 x 8tr x4ar%3D8 x 81( 10 ) x4m( 10ア1.6 cm's%3DAlternative Solution:V =dtAPdt4n( 10 drdr%3!50xdtA =4nrdAdr8ardt8n( 10)%3D50m1.6 cm's'%3D

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