For youth basketball, the baseline of the court measures 42 feet while the sideline stretches 50 feet. There is a circle in the middle of the court that has a diameter of 120 inches. The team can fit 17 people in the circle at one time. How many people can fit on the court?

To determine how many people can fit on the court, we need to calculate the area of the court and the area of the circle, then use the given information to estimate the number of people that can fit.

### Step 1: Calculate the Area of the Court
The court is rectangular in shape, with a baseline (length) of 42 feet and a sideline (width) of 50 feet.

\[
\text{Area of the court} = \text{length} \times \text{width} = 42 \, \text{feet} \times 50 \, \text{feet} = 2100 \, \text{square feet}
\]

### Step 2: Calculate the Area of the Circle
The diameter of the circle is 120 inches. First, we convert this measurement to feet, since our court area is in square feet.

\[
120 \, \text{inches} = \frac{120}{12} \, \text{feet} = 10 \, \text{feet}
\]

The radius of the circle is half of the diameter:

\[
\text{Radius} = \frac{10 \, \text{feet}}{2} = 5 \, \text{feet}
\]

The area of the circle is given by the formula:

\[
\text{Area of the circle} = \pi \times \text{radius}^2 = \pi \times (5 \, \text{feet})^2 = 25\pi \, \text{square feet}
\]

### Step 3: Calculate the Area per Person in the Circle
We know that 17 people can fit in the circle. Therefore, the area per person is:

\[
\text{Area per person} = \frac{\text{Area of the circle}}{17} = \frac{25\pi \, \text{square feet}}{17} \approx 4.63 \, \text{square feet per person}
\]

### Step 4: Calculate the Number of People that Can Fit on the Court
Now, we use the total area of the court and divide it by the area required per person.

\[
\text{Number of people on the court} = \frac{\text{Area of the court}}{\text{Area per person}} = \frac{2100 \, \text{square feet}}{4.63 \, \text{square feet per person}} \approx 453.14
\]

Since we cannot have a fraction of a person, we round down to the nearest whole number:

\[
\text{Number of people} = 453
\]

Therefore, approximately 453 people can fit on the court.

Would you like more details or have any questions? Here are some additional related questions to explore:

1. What is the perimeter of the basketball court?
2. How would the number of people change if the diameter of the circle increased to 15 feet?
3. What is the circumference of the circle in the middle of the court?
4. How much area does each person occupy if only 15 people can fit into the circle instead of 17?
5. If the sideline was reduced to 45 feet, how would that affect the number of people that can fit on the court?
6. How does changing the shape of the court to a square impact the area calculation?
7. What is the ratio of the circle's area to the court's area?
8. How many people can fit on the court if the circle was removed entirely?

**Tip:** When working with areas and conversions, always ensure your units are consistent to avoid errors in calculations.

Learn how to calculate how many people can fit on a youth basketball court based on dimensions and circle area. This problem involves calculating the area of a rectangle (court) and a circle (middle circle), and understanding how many people can fit inside the circle. Suitable for Grades 7-9.

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