What is the area of the target that earns at least 30 points on a throw?

Select the correct from the drop-down menu.

The area is 

     16  49  121  144 (choose one)

𝜋 square inches.

To determine the correct area of the target that earns at least 30 points on a throw, let's summarize the calculations:

1. **Area of the 50-point region**:
\[ A_{50} = \pi (3)^2 = 9\pi \]

2. **Area of the 40-point region**:
\[ A_{40} = \pi (7)^2 - \pi (3)^2 = 49\pi - 9\pi = 40\pi \]

3. **Area of the 30-point region**:
\[ A_{30} = \pi (11)^2 - \pi (7)^2 = 121\pi - 49\pi = 72\pi \]

Combining these, the total area for regions scoring at least 30 points is:
\[ A_{\geq 30} = 72\pi + 40\pi + 9\pi = 121\pi \]

So, the correct area is \( 121\pi \) square inches.

**Correct choice from the drop-down menu: 121**

Would you like more details or have any questions?

Here are some related questions to explore further:

1. What is the total area of the entire target?
2. How much area does each scoring region occupy individually?
3. What is the probability of hitting the exact center (50 points) of the target?
4. How would the probabilities change if the regions had different widths?
5. How do these calculations change if the dartboard is not hit uniformly?
6. If the width of each region was doubled, what would the new areas be?
7. What is the probability of scoring exactly 40 points?
8. How does the concept of expected value apply to Jake’s decision-making?

**Tip**: When solving probability problems involving geometric shapes, always break down the area calculations step by step to avoid errors.

Discover how to calculate the area of the dartboard regions scoring at least 30 points, including step-by-step calculations using circle area formulas. Suitable for students in Grades 7-9 interested in geometry and circle area calculations.

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