Question

Show your work Round to the nearest whole number if needed

Answer 1

Given:

Radius, r = 6

Let's find the chance of hitting the shaded area by finding the ratio.

Since the radius of the cirlce is 6, the length of one side of the square is the diameter:

s = 6 x 2 = 12

To find the ratio divide the area of the circle by area of the square. The area of the circle is the shaded area while the area of the square is the total possible area.

Thus,we have:

`\text{ Area of circle = }\pi r^2=3.1416\ast6^2=3.1416\ast36=113.0976\text{ square units}`
`\text{ Area of square = }s^2=12^2=12\ast12=144\text{ square units}`
`\text{ Ratio=}\frac{shaded\text{ area}}{total\text{ possible area}}=\frac{area\text{ of circle}}{area\text{ of square}}=(113.0976)/(144)=0.7854\approx0.79`
`\text{ Percentage ratio = 0.7854 }\ast\text{ 100=}78.54\text{ \%}`

Therefore, the chance of hitting the shaded region is 78.54%

ANSWER:

78.54%