Carcass wrote:
Attachment:
GRE exam - In the diagram above, B is the center of the larger circle. .jpg
In the diagram above, B is the center of the larger circle. AB is the radius of the larger circle and the diameter of the smaller circle. The shaded area is what fraction of the larger circle?
Enter your answer as a fraction. Fractions do not need to be in their simplest forms.
Let
r = radius of SMALLER circle
So,
2r = radius of LARGER circle (since the diameter of the SMALLER circle = radius of LARGER circle)
Area of circle: π(radius)²Area of SMALLER circle = π
r²
Area of LARGER circle = π(
2r)² =
π4r²Area of shaded part = area of LARGER circle - area of SMALLER circle
=
π4r² - π
r²
= π(4r² - r²)
= π3r²
The shaded area is what fraction of the larger circle?Faction = π3r²/π4r² = 3/4
Answer: 3/4
Cheers,
Brent
_________________
Brent Hanneson - founder of Greenlight Test Prep