## anonymous one year ago Linda throws a dart that hits the square shown below: A square is drawn. A circle of radius 9 units touches the sides of the square. What is the probability that the dart hits a point in the circle? 18% 21.5% 78.5% 81%

1. anonymous

2. anonymous

@TheSmartOne Anyone?

3. mathstudent55

|dw:1435684160450:dw|

4. mathstudent55

You need to find the area of the square and the area of the circle.

5. anonymous

cOuld u help me with that i thought my answer was going to be 21.5%

6. mathstudent55

Since you know the dart hit the square, the total outcome is the area of the square. The desired outcome is the area of the circle. $$P(hitting~ the ~circle) = \dfrac{area~of~circle}{area~of~square}$$

7. mathstudent55

The square has a half side of 9 units. What is the side of the square? What is x in the figure below? |dw:1435684401233:dw|

8. anonymous

it would have to be 78

9. mathstudent55

The radius of the circle is 9. The side of the square is the same as the diameter of the circle. If a circle has a radius of 9, what is its diameter?

10. mathstudent55

$$P(hitting~ the ~circle) = \dfrac{area~of~circle}{area~of~square}$$ $$= \dfrac{\pi r^2}{s^2}=\dfrac{\pi (9)^2}{18^2} = \dfrac{81 \pi}{324} \approx \dfrac{254.34}{324} = 0.785 = 78.5\%$$

11. mathstudent55

You are correct.