Geometry Problems

[Celsion]

Solving solids of revolutions around the x- or y-axis?

Example: The 59th problem of 2007- UIL B.

Square and semicircle problems?

Example: The 60th problem of 2007- UIL B.

[bradp]

Solids of revolution..

the function for that is... f(x) = -(4/3)(abs(x-3)) + 4

area under the curve of that function would be (for TI-83) fnInt(f(x),x,0,6)
volume when rotated around y-axis fnInt(2(pi)xf(x),x,0,6)

2(pi)x is the height of the solid of revolution if you think about turning it into a triangular prism from a triangular circle thing.

no I'm not going to use LaTeX

triangle/circle

center of circle = C
point of tangency = D

find AC and then AD using triangle stuff then find BD w/ similar triangles

[Celsion]

59) I'm probably doing something wrong for the solids of revolution and get a negative volume.

[unparseable or potentially dangerous latex formula]

60) Would angle ADC form a right angle?

[Quelloquialism]

[Kurt]

By the way, he only ever revolves the function around the y-axis for some reason.

So you can safely assume it is [unparseable or potentially dangerous latex formula] for any question on there.

Although it would be nice if he would change it up a bit. :D


Also, I find it quicker for some linear functions to simply think of it as combinations of cones/cylinders/frustums.

[Celsion]

Yeah, I knew something was wrong. I'm trying to practice all types of geometry problems in preparation for district. I just hate stated problems, too long to read. Thanks for all of the help.