Question

I need help with this worksheet it saids. a golf ball is hit and soft on the green a prize is won if it stops in the painted Circle the diameters of the green and circle are shown at the right at the ball is equally likely to stop on any part of the green what is the probability that prizes won.

Answer 1

Check Explanation

Step-by-step explanation

Since it has been provided in the question that prices are won if one hits a ball and it lands on the smaller circle or the painted part.

The probability of winnining a prize can then be given as the area of the painted region (that is, the painted circle) divided by the total area of the landing region possible (that is, the green circle).

Let the radius of the painted region or the painted circle be r

Let the radius of the green circle be R

Noting that the area of a circle = π (Radius)²

`\begin{gathered} \text{Probability of winning a prize = }\frac{Area\text{ of painted circle}}{Area\text{ of green circle}} \\ =(\pi r^2)/(\pi R^2) \\ =(r^2)/(R^2) \\ In\text{ percentage} \\ =(r^2)/(R^2)*100\text{ percent} \end{gathered}`

The final answer is evident from this, we just need to put in the dimensions of the radius of the painted circle (r) and the radius of the green circle (R).

Hope this Helps!!!