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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 2^{2} = 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 3^{2} = 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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