Question

Show your work. write answer as a percent and round the nearest whole number if needed.

Answer 1

the chance of hitting the shaded area is 6%

Step-by-step 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

`\begin{gathered} \frac{shaded\text{ }area}{total\text{ }possible\text{ }area}\text{= }(25\pi/4)/(100\pi) \\ =\text{ }(25\pi)/(4)/\text{ }100\pi \end{gathered}`
`\begin{gathered} \text{ =}(25π)/(4)*\text{ }\frac{1}{\text{ }100\pi}=\frac{\text{ }25\pi}{400\pi} \\ =\text{ 0.0625} \\ In\text{ percent = 0.0625}*100 \\ ratio=6.25\text{ \%} \end{gathered}`

To the nearest whole number, the chance of hitting the shaded area is 6%