SOLUTION: Water is being poured at the rate of 15cm3/sec into an inverted cone with a diameter of 3m and a height of 6m. At what rate is the surface rising just as the tank is filled?

Question 1193216: Water is being poured at the rate of 15cm3/sec into an inverted cone with a diameter of 3m and a height of 6m. At what rate is the surface rising just as the tank is filled?
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

The volume of the cone is

We are given dV/dt; we need to determine dh/dt. So we need to express the volume as a function of h only.

The full cone has height 6 and diameter 3, so its radius is 1.5. Since the sides of the cone are straight, the radius is always 1/4 of the height.

At the moment the cone is filled, the height h is 6, and

ANSWER: Just as the tank is filled, the water is rising at a rate of cm/sec

RELATED QUESTIONS
Water is leaking out of an inverted conical tank at a rate of 10000cm^3/min at the same... (answered by scott8148)

Water is being poured at the rate of 2pi cubic meter per minute into an inverted conical (answered by KMST)

Water is leaking out of an inverted conical tank at a rate of 10,500 cm3/min at the same... (answered by ikleyn,greenestamps)

water is leaking out of an inverted tank at a rate of 11200 cubic centimeters per min at... (answered by ikleyn)

A chemical is poured into a tank the shape of a cone with vertex down at the rate of 1/5... (answered by Alan3354)

Dry sand is being poured into a conical pile at a rate of 10 cubic meters per minute; the (answered by KMST)

The vertical angle of an inverted cone is 90 degrees. Water is poured into the cone to a... (answered by greenestamps)

An ice cream cone is made of an inverted cone with diameter 16 cm and slant height 17 cm, (answered by ankor@dixie-net.com)

.An inverted square pyramid has a height equal to 8m and a top edge equal to 3m.... (answered by ikleyn)