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IB Mathematics HL– Calculus, Differentiation, Related Rates, Rate of change

How can we solve the following related rates word problem?

“A conical water tank with vertex down has a diameter of 6 meters at the top and a height of 10 meters. If water flows out of the tank at a rate of , how fast is the water level falling when the water is 2 meters deep?”

Thanks

How can we solve the following related rates word problem?

“A conical water tank with vertex down has a diameter of 6 meters at the top and a height of 10 meters. If water flows out of the tank at a rate of , how fast is the water level falling when the water is 2 meters deep?”

Thanks

- Max
**Posts:**0**Joined:**Mon Jan 28, 2013 8:06 pm

IB Maths HL – Calculus, Implicit Differentiation, Related rates, Rate of change.

The steps for solving Relates Rates word-problems are:

1. Carefully read the problem (what is asked for, and what is given)

2. Draw a diagram

3. Use appropriate variables to represent the quantities involved in the problem. Write down all equations that relate these variables and other given constants (e.g. Pythagorean Theorem, similar triangles, area, volume, proportions, trigonometric functions)

4. Differentiate both sides of the final equation with respect to time. This usually involves implicit differentiation.

5. Plug in given values and solve!!

Concerning you question,

Let represent the volume and represent the radius of the tank.

We know that

The volume of the cone is given

.

By similar triangles,

So the volume of the cone can be written

Differentiating with respect to time:

(1)

Now plug everything in to equation (1) and solve for :

meters per minute

Hope these help!!

The steps for solving Relates Rates word-problems are:

1. Carefully read the problem (what is asked for, and what is given)

2. Draw a diagram

3. Use appropriate variables to represent the quantities involved in the problem. Write down all equations that relate these variables and other given constants (e.g. Pythagorean Theorem, similar triangles, area, volume, proportions, trigonometric functions)

4. Differentiate both sides of the final equation with respect to time. This usually involves implicit differentiation.

5. Plug in given values and solve!!

Concerning you question,

Let represent the volume and represent the radius of the tank.

We know that

The volume of the cone is given

.

By similar triangles,

So the volume of the cone can be written

Differentiating with respect to time:

(1)

Now plug everything in to equation (1) and solve for :

meters per minute

Hope these help!!

- miranda
**Posts:**268**Joined:**Mon Jan 28, 2013 8:03 pm

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