Dominic is building a bench with a seat in the shape of a trapezoid. One base is 5 feet. The other base is 4 feet. The perpendic
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Answer:
- <u>0.075 m/min</u>
Explanation:
You need to use derivatives which is an advanced concept used in calculus.
<u>1. Write the equation for the volume of the cone:</u>
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<u>2. Find the relation between the radius and the height:</u>
- r = diameter/2 = 5m/2 = 2.5m
- h = 5.2m
- h/r =5.2 / 2.5 = 2.08
<u>3. Filling the tank:</u>
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:
<u>4. Find the derivative of the volume of water with respect to time:</u>
<u>5. Find x² when the volume of water is 8π m³:</u>
m²
<u>6. Solve for dx/dt:</u>
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<u>7. Find dh/dt:</u>
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.