Question

Sand falls from an overhead bin and accumulates in a conical ple with a radius that is always four times its height Suppose the height of the pile increases at a rate of 2 cm/s when the pile is 15 cm High Al whatrate is the sand leaving the bin at that instant? Let V and be the volume and height of the cone, respectively Write equation that relates and hand does not include the radius of the con Type an exact answer, using as needed)

Answer 1

Let h and a height and radius of the pile respectively Then given 8= 4h At the instant h=15cm dh dt 2 cmls Forst know volume of conical pile, و بيا V = 1/3 Trzh put 8=4h r= 4h , we get IT (4h)² h 3 -) 16 Thi 3 3 To find rate of volume adding/ leaving , differentiate with respect to t

- dv dt det (Is Th =) dv dt 167 d 3 dat d (23) Applying chain sule / 2 dv 16 = T d line) det. da dh ch dt -) dv dt 16 TT (36²) dh dt -) du - 1677 16T h² dh det put h=15 cm and a 2 emis = we get dt du It 16 TT (15)? (2) 7200 TT cm m?/sec cm²/sec 22619.49 cm3

Note - dz.") dir n2-1

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