Wednesday, February 18, 2015

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.

How to get started: The formula for the area of a circle (which you probably know anyway) is given in that box of math facts at the beginning of the section

Since we know what the radius is, finding the area of the whole circle is easy enough

Unfortunately, the question didn’t ask for the area of the whole circle; it asked for the area of the shaded region. So we need to figure out what part of the circle this forty degree section represents.

The same box that gave us the formula for a circle also tells us how many degrees are in a circle (360) which makes it fairly easy to figure out what part of the circle forty degrees represents.

The shaded part therefore represents one ninth of the area we just figured out.

1 comment:

  1. I'd suggest adding something to the end about checking the fraction to see whether it can be simplified.

    Sometimes kids get this far but don't see their answer in the options available and conclude that they have done something wrong and then they lose confidence in what they are doing.

    (And I'd actually show the step 1/9 * 49pi = 49pi/9 )