Volumes of solids using cross sections and get a 100 on the assessment

Get ready for the assessment on Tuesday!

Things and tips you have to know about finding volumes of solids using cross sections.

For example:  The base of a solid is the region enclosed by the circle x^2 + y^2 =16. Cross-sections
perpendicular to the x-axis are equilateral triangles.

1. Find the key words:

In this given information, cross-sections ... to x-axis and equilateral triangles are key words.

a. Cross- sections.. to x-axis= use dx
    Cross-sections..to y-axis= use dy

b. equilateral triangles= the area formula that needed to be used is 1/2bh

2. Draw out the diagram: It gives you a picture of how does the base of the solid looks like.


（Stole from Mrs. Wahl on google drive)












3. Find out the equation by only contain x in this problem or if it is needed, use substitution on the other problems.

y^2= 16-x^2
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Tips in general:

4. Study the basis formulas for geometry 

5. Proportion of the length for right triangles.
   
        3,4,5 /  1, square root of 3, 2 / 1,2, square root of 5 /5,12,13/ 7,24,25/

6. Do not take the square root sign out of a plus or minus equation.

      For example: y^2= 9-x^2 but we need to find the equation in term of y
                            x^2= 9-y^2
                            x= square root of 9-y^2

        normally we can write it as x= 3-y, but in here we can not !

7. Reading the questions carefully and do not get confused with the information that we do not need at all ! 

For example: the equation of f(x) which is given on the fourth FRQ in practice 3. 

Good luck on Tuesday!