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A water tank has the shape of a right circular cone with its vertex down. Its altitude is 10 cm and theradius of the base is 15 cm. Water leaks out of the bottom at a constant rate of lcu.cm/sec. Water ispoured into the tank at a constant rate of C cu. cm/sec. Compute C so that the water level will berising at the rate of 4 cm/sec at the instant when the water is 2 cm deep. |
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Answer» Altitude of cone=10cm and radius of base=15cm. Volume of cone=`1/3pir^2h` by similarity radius of small cone when water is 2cm deep is `3/2h`cm. volume of cone=V=`1/3pi9/4xxh^2xxh=(3pih^3)/4``(dv)/dt=9pih^2xx(dh)/dt` given`(dh)/dt=4cm` and h=2cm. =>`(dv)/dt=36pi=C-1` =>C=`(36pi+1)(cm)^3` |
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