Agnes and I were at Borders the other day and I came across a calendar that they were selling for the new school year. It was the SAT Question of the Day 2009 calendar. On the back of the calendar was this math question, which I thought was harder than I remember SAT questions.
The circle shown above has center O and a radius of length 5. If the area of the shaded region is 20pi, what is the value of “x”?
- 18
- 32
- 45
- 54
- 72
Note: the figure is not drawn to scale.
The College Board website has this same question here if you want to check your answer. Let me know if you were able to figure it out.
You can also sign up to receive ongoing SAT Questions of the Day at the same site.
August 19th, 2008 at 3:00 pm
Had to dust off my brain to figure it out, and indeed it was a joint effort with my officemate, but that was the most fun we’ve had all day…
What does that say about our JOBS…
I don’t remember SAT questions being that hard either!
September 1st, 2008 at 9:43 am
Remember that kids can use calculators on the SAT these days. That makes the reverse engineering of the area of the shaded area to find the arc much easier. Once you know the arc it is simply remembering that then sum of the interior angles equal to 180.
Doing it without a calculator is difficult.
September 1st, 2008 at 9:47 am
On second thought without a calcluator is not that hard either. LOL, but considering that kids are trained with a calculator, it is probably faster.
October 14th, 2008 at 3:30 am
Hee hee! That *was* fun!
Man, remember how we stressed about that test?
July 31st, 2009 at 8:41 am
Ok,this is one of the easiest problems I have seen for the S.A.T. It’s like a gift. All you need to do is these steps:
1.) Set up the formula for area of a sector n/360 x area of the circle(25pi)=20pi
2.) Solve for n and you get n=288
3.) Measure of interior angles in a circle=360,hence 360-288=72 degrees for the angle adjacent to the 90 degree one in the triangle(the unlabeled one).
4.) Sum of angles in a triangle=180 and so 72+90=162
5.) 180-162=18 degrees
6.) x=18
Problem Solved!
P.S.: Calculator is not needed, this involves simple math and I could do this in my head. :]
October 4th, 2009 at 3:25 pm
Hey,
I got A. 18. You just have to remember that the area of a sector is (pi x r^2) * theta/360. We know that the radius is 5, and the area of the sector is 20*pi. We could find that theta is 288. Then, just subtract that from 360 to get 72 degrees. That angle of the triangle is complimentary to the angle of x, so x equals 18.
October 11th, 2009 at 5:36 pm
Guys/Girls,
That question was fairly complicated but if you think about it, it is not the hardest question in the world. If you think of it in a linear way, it is very simple. When I took the SAT, (when the scores were out of 1600) every math question was like this. PRACTICE if you think this is hard.