A figure shows a circle and 2 identical quadrants. The diameter of circle is 28cm.Find the area of shaded part

To solve this problem, we'll go step by step:

1. **Identify the given information:**
   - The diameter of the circle is given as 28 cm.

2. **Calculate the radius of the circle:**
   \[
   \text{Radius} = \frac{\text{Diameter}}{2} = \frac{28}{2} = 14 \text{ cm}
   \]

3. **Calculate the area of the circle:**
   \[
   \text{Area of the circle} = \pi r^2 = \pi \times 14^2 = 196\pi \text{ cm}^2
   \]

4. **Area of one quadrant:**
   Since the quadrants are identical and each is one-fourth of a circle with radius equal to the radius of the given circle:
   \[
   \text{Area of one quadrant} = \frac{1}{4} \times \pi r^2 = \frac{1}{4} \times \pi \times 14^2 = 49\pi \text{ cm}^2
   \]

5. **Calculate the total area of the two quadrants:**
   \[
   \text{Total area of two quadrants} = 2 \times 49\pi = 98\pi \text{ cm}^2
   \]

6. **Calculate the area of the shaded region:**
   The shaded part is the area of the circle minus the total area of the two quadrants.
   \[
   \text{Area of the shaded region} = 196\pi - 98\pi = 98\pi \text{ cm}^2
   \]

7. **Final answer:**
   \[
   \text{Area of the shaded region} \approx 98 \times 3.14 = 307.72 \text{ cm}^2
   \]

So, the area of the shaded part is approximately **307.72 cm²**.

Would you like more details or have any questions?

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Here are 8 related questions you might find interesting:

1. What is the area of the circle if the diameter is doubled?
2. How would the area of the shaded part change if the quadrants were not identical?
3. What is the perimeter of the shaded region?
4. How does the area of the shaded part change if the radius is halved?
5. What is the ratio of the shaded area to the total area of the circle?
6. How would the area change if the circle had a different radius?
7. Can you derive the formula for the area of the shaded region for any circle?
8. What would happen to the shaded area if there were three quadrants instead of two?

**Tip:** Always remember that the area of a quadrant is a quarter of the area of a full circle, which can simplify many calculations!

Learn how to calculate the area of the shaded region in a circle with two identical quadrants. Step-by-step solution provided, covering the area of a circle and the area of quadrants. Suitable for high school students.

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