Standardized test prep -- Another circle problem

[Another SAT/GRE style geometry problem, slightly more advanced than the last one.]

The circle pictured here has radius 5 with a center indicated by the black dot. What is the area of the shaded region?

How to get started: You may have already thought of this own your own (it’s OK to get ahead of the class here), but if you’re stuck, it’s often a good idea  to ask yourself “is there a simpler related question I can answer?” In this case, how about finding the area of the whole circle?

Now we just need to figure out what part of the circle is shaded. Since the angle corresponding to the shaded region is vertical with the angle that measures x degrees, x degrees is also the measure of that angle. That means that the ratio of x to 360 is the same as the ratio of the area of the shaded region to the area of the circle.

How do we figure out what x is? Look at the two labeled angles. Put together they form a straight line. That means that the two angles are supplementary.

That gives us x equals thirty and since thirty is one twelfth of 360…

The area of the shaded region is one twelfth the area of the circle.

Monday Video -- Möbius Maglev

[Every Monday for the next few months, we'll be posting a short video clip here at You Do the Math. All will have at least a tenuous connection to science, technology, engineering, or mathematics. Teachers can use these as writing prompts or as starting points for larger lesson plans (I'll try to include some hints now and then), but the main purpose is simply to have a little fun.]


Levitating Superconductor on a Möbius strip

Standardized test prep -- A simple circle problem

[I'm working on a larger project involving test prep for the math sections of tests such as the SAT and GRE. The exact details are still up in the air. I'm pretty sure that there will be various online components but the details are very much still in flux. In the meantime, I'll be posting some examples to get the ball rolling.]

The circle pictured here has radius 7. Find the shaded area.

Monday Video -- very slow lightning

[Every Monday for the next few months, we'll be posting a short video clip here at You Do the Math. All will have at least a tenuous connection to science, technology, engineering, or mathematics. Teachers can use these as writing prompts or as starting points for larger lesson plans (I'll try to include some hints now and then), but the main purpose is simply to have a little fun.]


Three Strokes of Upward Lightning

Monday Video -- Human-Powered Helicopter

[Every Monday for the next few months, we'll be posting a short video clip here at You Do the Math. All will have at least a tenuous connection to science, technology, engineering, or mathematics. Teachers can use these as writing prompts or as starting points for larger lesson plans (I'll try to include some hints now and then), but the main purpose is simply to have a little fun.]


Atlas Human-Powered Helicopter - AHS Sikorsky Prize Flight