## 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

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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2 weeks 2021-09-15T09:04:10+00:00 1 Answer 0

• 0.075 m/min

Explanation:

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:

• r = diameter/2 = 5m/2 = 2.5m
• h = 5.2m
• h/r =5.2 / 2.5 = 2.08

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

• x/y=r/h
• y = x . h / r

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: 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.