Question

A conical tank (w/ vertex down) is 10 ft across the top and 12 ft deep. If the water is flowing into the tank at the rate of 10 cubic feet per min. find the rate of change of the depth of the water the instant it is 8 ft deep

Answer 1

Can you write an equation expressing the rate at which the height of the water is rising? (Hint: Use Volume)

Answer 2

i got at far as this: \[DV/Dt=\pi/3(r ^{2}dh/dt+2rhdr/dt)\]

Answer 3

i think dv/dt is -10cubic feet/min so i would substitute that but what is dh/dt and dr/dt

Answer 4

You'll have to use similar triangles to figure those out. Find a ratio of the given cone and then the cone of water that is inside that cone

Answer 5

i don't understand