Question

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.

Answer 1

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`