Math Problem





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Discus: SAT/ACT Tests and Test Preparation: May 2003 Archive: Math Problem
By Tylerf (Tylerf) on Wednesday, April 30, 2003 - 09:59 pm: Edit

10 real SAT's
test 4
section 1
problem 25

The explanation is missing from the site I use, and I need an explanation. Thanks.

By Incognito (Incognito) on Wednesday, April 30, 2003 - 10:07 pm: Edit

When you double the angle, the area of the arc is also doubled. So, the change in area is related to a change in the angle measure by multipication. Multiply the angle by 3, and the are of the arc is 3 times greater.

The area of the circle itself, on the other hand, is a different story. When you increase the radius, the corresponding increase in the area of the arc is much greater. When you double the radius, you "quadruple" the area of the arc, because 22 = 4.

Here's an example:
Let's just say that the radius of a circle is 1. The area is thus pi(1)2 = pi(1). Now, if you double that radius, the area becomes pi(2)2 = pi(4). The area has increased exponentially. If you were to triple the radius, then the area would be multiplied by 32 = 9.

By Incognito (Incognito) on Wednesday, April 30, 2003 - 10:18 pm: Edit

In this case, I believe you double the angle and the radius, so you'd first multiply 3 by 2 (angle) = 6, and then multiply 6 by 4 (since the radius doubles), and you get 24 = choice A. A pretty hard question for an SAT I, I must admit.

By Xiggi (Xiggi) on Thursday, May 01, 2003 - 12:59 am: Edit

It was so hard that Study Hall decided to pass it up

:)

By the way, Incognito, check your email.


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