Calculate  the area  of the shaded  sector  90 and 14 centimeters 

The area of a sector of a circle can be calculated using the formula:

\[
\text{Area of Sector} = \frac{\theta}{360^\circ} \times \pi r^2
\]

Where:
- \(\theta\) is the angle of the sector (in degrees),
- \(r\) is the radius of the circle.

For this problem:
- \(\theta = 90^\circ\) (the given angle),
- \(r = 14 \, \text{cm}\) (the radius).

Now, applying the values:

\[
\text{Area of Sector} = \frac{90}{360} \times \pi \times 14^2
\]
\[
\text{Area of Sector} = \frac{1}{4} \times \pi \times 196
\]
\[
\text{Area of Sector} = \frac{196\pi}{4}
\]
\[
\text{Area of Sector} = 49\pi
\]

Using \(\pi \approx 3.1416\):

\[
\text{Area of Sector} \approx 49 \times 3.1416 = 153.9384 \, \text{cm}^2
\]

So, the area of the shaded sector is approximately \(153.94 \, \text{cm}^2\).

Would you like any further details or clarifications?

Here are five related questions:
1. How does the area change if the angle is doubled?
2. What would be the area of a full circle with the same radius?
3. How is the formula for sector area derived from the area of a circle?
4. If the radius is halved, what would be the new sector area?
5. Can you calculate the perimeter of the sector, including the arc length?

**Tip:** The sector area is directly proportional to the central angle; doubling the angle will double the area.

Calculate the area of the shaded sector 90 and 14 centimeters

Learn how to calculate the area of a 90° shaded sector with a radius of 14 cm using the sector area formula. This step-by-step solution is ideal for students in Grades 8-10, covering geometry concepts related to circles and sector areas.

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