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,
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:
Now plug everything in to equation (1) and solve for
meters per minute
Hope these help!!