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peachfuzz
Bunuel
If the area of circle O is 16π, what is the length of an arc on the circle formed by a central angle measuring 45 degrees?

A. π
B. 3π/2
C. 2π
D. 5π/2
E. 8π

Area=16π
radius=4

8π / 4 = 2π

C. 2π

Hi peachfuzz,

You have to be careful when dealing with certain GMAT prompts - sometimes the wrong answers are answers to DIFFERENT questions. If you're not properly paying attention to the details in the prompt (and what the question specifically ASKS for), then you might select one of the wrong answers and not even realize it.

Here, the prompt asks for the arc length of a 45 degree piece of the circle (NOT a 90 degree piece). Since 45 degrees is 1/8 of a circle, you need to divide by 8 (and not 4).

GMAT assassins aren't born, they're made,
Rich
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are is given it means that so we can conlude that
radious = 4

now we have been asked that arc form ny an 45 angle .
we know that length of an arc =2pie r 45/360 so 2xpiex4x45/360= pie
answer is A
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Bunuel
If the area of circle O is 16π, what is the length of an arc on the circle formed by a central angle measuring 45 degrees?

A. π
B. 3π/2
C. 2π
D. 5π/2
E. 8π

Let’s first determine the radius of the circle. Since the area is 16π:

Area = π x radius^2

16π = π x radius^2

16 = radius^2

radius = 4

Since circumference = 2π(radius), the circumference = 8π.

We need to determine the length of an arc on the circle formed by a central angle measuring 45 degrees.

We can create the following proportion to determine the length of the arc (which we denote as x):

45/360 = x/8π

1/8 = x/8π

8x = 8π

x = π

Answer: A
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area = 16π
πr^2=16π
r=4
circumference = 2πr
=8π
area of 45 degrees arc = circumference x (45/360)
= 8π x (45/360)
= π
IMO - A
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