Question

A circle of radius 12 cm has a sector with a central angle of 90°. Find the area of the minor segment formed by the chord of the sector. Pi = 3.14

• A. 41.04 cm²
• B. 36.52 cm²
• C. 45.18 cm²
• D. 39.24 cm²

Answer 1

Answer:

A. 41.04 cm²

To find the area of the minor segment with $\pi = 3.14$, we follow the same formula: subtracting the area of the triangle from the area of the sector.

Given Data:

• Radius ($r$) = $12\text{ cm}$

• Central Angle ($\theta$) = $90^\circ$

• Value of $\pi$ = $3.14$

Step-by-Step Calculation:

1. Calculate the area of the sector:

   
   

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

   $\text{Area of Sector} = \frac{90^\circ}{360^\circ} \times 3.14 \times (12)^2$

   $\text{Area of Sector} = \frac{1}{4} \times 3.14 \times 144$

   $\text{Area of Sector} = 3.14 \times 36 = 113.04\text{ cm}^2$

2. Calculate the area of the triangle:

   
   

   $\text{Area of Triangle} = \frac{1}{2} \times r^2 \sin(\theta)$

   $\text{Area of Triangle} = \frac{1}{2} \times 12 \times 12 \times \sin(90^\circ)$

   $\text{Area of Triangle} = \frac{1}{2} \times 144 \times 1 = 72\text{ cm}^2$

3. Calculate the area of the minor segment:

   
   

   $\text{Area of Minor Segment} = \text{Area of Sector} - \text{Area of Triangle}$

   $\text{Area of Minor Segment} = 113.04 - 72 = 41.04\text{ cm}^2$

Answer:

The area of the minor segment is $41.04\text{ cm}^2$.