Learning Resources
Lesson
The object of this project is to find a cone shaped water cup that will hold maximum volume. To do this you must model the problem with simply constructed water cups and doing the various measurements required in the questions posed. To view the construction of such a circle click here.
You may work with a partner or work on your own to complete this project. You will require the following materials to complete the project:
- a circle as constructed above
- ruler to measure height and radius
- volume can be measured by formula
where A represents the area of the base or by filling the cones with sand, sugar, or some other pour able substance available. The material can be poured form the cone into a measuring cup and the millilitres and cubic centimetres can be equated.
- tape measure to find the circumference or use the formula
- the formula for area of a Circle
To complete (a) to (c) use a table; Click here to view a table than can be used. You may print this table by right clicking within the window and choose print from the pop up menu.
Since Question (f) may be confusing for you and it is needed in later versions of this project make note of the following hint to find the function.
Remember to write a function for the area of the base of a cone you must use the formula for the area of a circle which is . In this case we want an expression for the radius in terms of the total percent of the original circle that was removed. The radius of the base decreases by 1 cm for each 10% of the circle that is removed which means that for every 1% of the circle removed the radius of the base will decrease by 0.1 cm. The radius of the base can be expressed as 
where x represents the percentage of the circle remove. Now using the formula write the area of the base as a function of x .
Use your function to find the required rates of change.
Complete the questions in the Activities section of the lesson !
Activity
Manufacturing Water Cooler Cups p.83 - 84. Complete (a) to (g) inclusive
Test Yourself
There is no self test for this lesson.