the chance of hitting the shaded area is 6%
Explanation:
diameter of shaded region = 5 in
Diameter = 2(radius)
radius = diameter/2 = 5/2 in
Diameter of unshaded region = 20 in
radius = 20/2 = 10 in
Area of circle = πr²
Area of shaded region = π × (5/2)² = 25π/4
Area of unshaded region = π × 10² = 100π
The chance of hitting the shaded area = shaded area/ total possible area
[tex]\begin{gathered} \frac{shaded\text{ }area}{total\text{ }possible\text{ }area}\text{= }\frac{25\pi/4}{100\pi} \\ =\text{ }\frac{25\pi}{4}\div\text{ }100\pi \end{gathered}[/tex][tex]\begin{gathered} \text{ =}\frac{25π}{4}\times\text{ }\frac{1}{\text{ }100\pi}=\frac{\text{ }25\pi}{400\pi} \\ =\text{ 0.0625} \\ In\text{ percent = 0.0625}\times100 \\ ratio=6.25\text{ \%} \end{gathered}[/tex]
To the nearest whole number, the chance of hitting the shaded area is 6%
