Questions: Find the area of the blue shaded region.

Find the area of the blue shaded region.
Transcript text: Find the area of the blue shaded region.
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Solution

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Solution Steps

Step 1: Calculate the Area of the Entire Circle

The radius of the circle is given as 6 cm. The formula for the area of a circle is: \[ \text{Area} = \pi r^2 \] \[ \text{Area} = \pi (6)^2 \] \[ \text{Area} = 36\pi \]

Step 2: Calculate the Area of the Sector

The angle of the sector is given as 150°. The area of a sector is given by: \[ \text{Area of Sector} = \left( \frac{\theta}{360} \right) \times \pi r^2 \] \[ \text{Area of Sector} = \left( \frac{150}{360} \right) \times 36\pi \] \[ \text{Area of Sector} = \left( \frac{5}{12} \right) \times 36\pi \] \[ \text{Area of Sector} = 15\pi \]

Step 3: Calculate the Area of the Blue Shaded Region

The blue shaded region is the area of the circle minus the area of the sector. \[ \text{Area of Blue Shaded Region} = 36\pi - 15\pi \] \[ \text{Area of Blue Shaded Region} = 21\pi \]

Final Answer

\[ \text{Area of Blue Shaded Region} \approx 21 \times 3.14 = 65.94 \, \text{cm}^2 \] Rounded to the nearest tenth: \[ \text{Area of Blue Shaded Region} \approx 65.9 \, \text{cm}^2 \]

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