Find the area of the shaded region in the figure. Use the pi key for pi.
7 "
3 and one half "
Question content area bottom
Part 1
The area of the shaded region in the figure is approximately

enter your response here
▼
in. squared
in.
​(Type an integer or decimal rounded to the nearest tenth as​ needed.)

To find the area of the shaded region, we need to interpret the figure, assuming it consists of two circles with different radii based on the measurements provided:

1. **Outer Circle**:
   - Radius = \(7\) inches
   - Area of the outer circle = \(\pi \times (7)^2 = 49\pi\) square inches

2. **Inner Circle**:
   - Radius = \(3.5\) inches (converted from "3 and one-half inches")
   - Area of the inner circle = \(\pi \times (3.5)^2 = 12.25\pi\) square inches

3. **Shaded Region**:
   - The shaded area is the area of the outer circle minus the area of the inner circle.
   - Area of the shaded region = \(49\pi - 12.25\pi = 36.75\pi\) square inches

Using \(\pi \approx 3.14159\),
\[
36.75 \pi \approx 36.75 \times 3.14159 \approx 115.5 \text{ square inches}
\]

### Answer:
The area of the shaded region is approximately **115.5 square inches**.

Would you like a detailed explanation of each step or have any questions?

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Here are five related questions you might consider:
1. How would the area change if the inner circle radius were doubled?
2. What is the difference in area if the outer radius were increased by 1 inch?
3. How would the area calculation change if we used different approximations of \(\pi\)?
4. What is the area of the shaded region if the inner circle were replaced by a square with the same area?
5. How would the problem change if the circles were concentric ellipses instead?

**Tip:** Always check if units are consistent throughout the problem to avoid calculation errors.

Find the area of the shaded region in the figure. Use the pi key for pi.
7 "
3 and one half "

The area of the shaded region in the figure is approximately

enter your response here
▼
in. squared

(Type an integer or decimal rounded to the nearest tenth as needed.)

Learn how to find the area of a shaded region between two concentric circles. This solution involves calculating the area of an outer circle with a radius of 7 inches and an inner circle with a radius of 3.5 inches. The answer is rounded to the nearest tenth, suitable for students in Grades 6-8.

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