A circle is inscribed in a square. Point Q in the square is chosen at random. What is the probability that Q lies in the shaded region?
Know | Need | Plan |
---|---|---|
The length of a side of the square, which is also the length of the diameter of the inscribed circle | The areas of the square and the shaded region | Subtract the area of the circle from the area of the square to find the area of the shaded region. Then use it to find the probability. |
The probability that Q lies in the shaded region is about 0.215, or 21.5%.
Archery An archery target has 5 colored scoring zones formed by concentric circles. The target's diameter is 122 cm. The radius of the yellow zone is 12.2 cm. The width of each of the other zones is also 12.2 cm. If an arrow hits the target at a random point, what is the probability that it hits the red zone?
How can you find the area of the red zone?
The red zone lies between two concentric circles. To find the area of the red zone, subtract the areas of the two concentric circles.
The red zone is the region between a circle with radius
The probability of an arrow hitting a point in the red zone is 0.12, or 12%.