Question:
A circle is divided into 16 identical sectors. If radius of the circle is 7 cm, area of each sector is
A circle is divided into 16 identical sectors. If radius of the circle is 7 cm, area of each sector is
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Calculating sector area can also be done using the central angle formula, but direct division is much faster and reduces decimal calculation errors!
Updated On: Jul 22, 2026
- \(\frac{77}{4} \text{ cm}^2\)
- \(77 \text{ cm}^2\)
- \(154 \text{ cm}^2\)
- \(\frac{77}{8} \text{ cm}^2\)
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The Correct Option is D
Solution and Explanation
Step 1: Understanding the Question:
The topic of this question is Areas Related to Circles.
A sector of a circle is a region bounded by two radii and an arc of the circle.
If a circle is divided into \(N\) identical (equal) sectors, the area of each individual sector is exactly \(\frac{1}{N}\) of the total area of the circle.
We are given a circle of radius \(r = 7\) cm divided into 16 identical sectors.
We need to calculate the area of each sector.
Step 2: Key Formula or Approach:
1. Calculate the total area of the circle using the standard formula:
\[ \text{Total Area} = \pi r^2 \] 2. Divide this total area by the number of identical sectors (16) to find the area of one sector:
\[ \text{Area of each sector} = \frac{\text{Total Area}}{16} = \frac{\pi r^2}{16} \] We will use the value of \(\pi = \frac{22}{7}\) to perform the calculations.
Step 3: Detailed Explanation:
• Calculate the total area of the circle with radius \(r = 7\) cm:
\[ \text{Total Area} = \pi r^2 \] \[ \text{Total Area} = \frac{22}{7} \times 7 \times 7 \]
• Simplify the expression by cancelling the common factor of 7:
\[ \text{Total Area} = 22 \times 7 = 154 \text{ cm}^2 \]
• Since the circle is divided into 16 identical sectors, calculate the area of each sector:
\[ \text{Area of each sector} = \frac{\text{Total Area}}{16} \] \[ \text{Area of each sector} = \frac{154}{16} \text{ cm}^2 \]
• Simplify the fraction by dividing the numerator and denominator by their greatest common divisor, which is 2:
\[ \text{Area of each sector} = \frac{154 \div 2}{16 \div 2} = \frac{77}{8} \text{ cm}^2 \]
Step 4: Final Answer:
The area of each sector is \(\frac{77}{8} \text{ cm}^2\).
Therefore, the correct option is (D).
The topic of this question is Areas Related to Circles.
A sector of a circle is a region bounded by two radii and an arc of the circle.
If a circle is divided into \(N\) identical (equal) sectors, the area of each individual sector is exactly \(\frac{1}{N}\) of the total area of the circle.
We are given a circle of radius \(r = 7\) cm divided into 16 identical sectors.
We need to calculate the area of each sector.
Step 2: Key Formula or Approach:
1. Calculate the total area of the circle using the standard formula:
\[ \text{Total Area} = \pi r^2 \] 2. Divide this total area by the number of identical sectors (16) to find the area of one sector:
\[ \text{Area of each sector} = \frac{\text{Total Area}}{16} = \frac{\pi r^2}{16} \] We will use the value of \(\pi = \frac{22}{7}\) to perform the calculations.
Step 3: Detailed Explanation:
• Calculate the total area of the circle with radius \(r = 7\) cm:
\[ \text{Total Area} = \pi r^2 \] \[ \text{Total Area} = \frac{22}{7} \times 7 \times 7 \]
• Simplify the expression by cancelling the common factor of 7:
\[ \text{Total Area} = 22 \times 7 = 154 \text{ cm}^2 \]
• Since the circle is divided into 16 identical sectors, calculate the area of each sector:
\[ \text{Area of each sector} = \frac{\text{Total Area}}{16} \] \[ \text{Area of each sector} = \frac{154}{16} \text{ cm}^2 \]
• Simplify the fraction by dividing the numerator and denominator by their greatest common divisor, which is 2:
\[ \text{Area of each sector} = \frac{154 \div 2}{16 \div 2} = \frac{77}{8} \text{ cm}^2 \]
Step 4: Final Answer:
The area of each sector is \(\frac{77}{8} \text{ cm}^2\).
Therefore, the correct option is (D).
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