## PLS TRY TO ANSWER ASAP. A water tank at a filtration plant is built in the shape of an inverted cone with height 5.2 m and diameter 5 m

Question

PLS TRY TO ANSWER ASAP.

A water tank at a filtration plant is built in the shape of an inverted cone with height 5.2 m and diameter 5 m at the top. Water is being pumped into the tank at a rate of 1.2 m³/min. Find the rate at which the water level is rising when there is 8π m³ of water

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2021-09-15T09:04:10+00:00
2021-09-15T09:04:10+00:00 1 Answer
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## Answers ( )

Answer:0.075 m/minExplanation:You need to use derivatives which is an advanced concept used in calculus.

1. Write the equation for the volume of the cone:2. Find the relation between the radius and the height:3. Filling the tank:Call y the height of water and x the horizontal distance from the axis of symmetry of the cone to the wall for the surface of water, when the cone is being filled.

The ratio x/y is the same r/h

The volume of water inside the cone is:

4. Find the derivative of the volume of water with respect to time:5. Find x² when the volume of water is 8π m³:m²

6. Solve for dx/dt:7. Find dh/dt:From y/x = h/r = 2.08:

That is the rate at which the water level is rising when there is 8π m³ of water.