Question

water flows into an inverted conical tank at the rate of 24cm^3/min. when the depth is 9cm, how fast is the level rising ? assume that the height of the tank is 15cm and radius at the top is 5 cm

Answer 1

Lets start with what we know v't=24, h=15, r=5, v=(1/3)pir^2h

Answer 2

Now we need to use similar triangles to find the ratio of the height of the tank to the radius. r/h=5/15 r = h(1/3) we want to find h' so we need to get rid of r if we were looking for r then we would rearrange for h to get h=3r.

Then we sub in h(1/3) for r in our formula for volume to get v=(1/3)pi(h(1/3))^2h. This simplifies to v=(1/3)pih^2(1/9)h and then simplifies further to v=(1/27)pih^3. Once we have this we need to use implicit differentiation. So v'=(1/9)pih^2h' and then we solve for h' to get h'=v'/((1/9)pih^2). Now we plug in our values h'=24/((1/9)pi(15)^2) plug that into a calculator and we have our answer. If you need me to explain anything further let me know =).

Answer 3

thank you very much for ur help!

Answer 4

no problem =)