Question

Distribution of total number of cellular phones sold by six stores in December, 2025 is given in the following pie chart.

What is the central angle corresponding to the total number of cellular phones sold by S?

• A. \( 99.2^\circ \)
• B. \( 93.6^\circ \)
• C. \( 105.6^\circ \)
• D. \( 97.4^\circ \)

Hint:

In pie-chart questions, remember the shortcut: \[ 1\% = \frac{360^\circ}{100} =3.6^\circ \] Therefore, \[ 26\% = 26 \times 3.6^\circ =93.6^\circ \] This method is often faster during examinations.

Answer 1

The Correct Option is B

Concept: A pie chart is a circular graphical representation of data in which the entire circle represents the total value or \(100\%\) of the data. Since a complete circle contains \(360^\circ\), each category occupies a sector proportional to its percentage share. The central angle corresponding to any category is calculated using: \[ \text{Central Angle} = \left( \frac{\text{Percentage of the Category}}{100} \right) \times 360^\circ \] This formula converts the percentage share into an equivalent angular measure.

Step 1: Identify the percentage share of store S. From the given pie-chart distribution: \[ \text{T}=20\%, \quad \text{U}=12\%, \quad \text{P}=14\%, \quad \text{Q}=10\%, \quad \text{R}=18\%, \quad \text{S}=26\% \] Therefore, \[ \text{Percentage corresponding to Store S} = 26\% \]

Step 2: Apply the formula for central angle. Using \[ \text{Central Angle} = \frac{\text{Percentage}}{100} \times 360^\circ \] Substituting the value of Store S: \[ \text{Central Angle} = \frac{26}{100} \times 360^\circ \] \[ = 0.26 \times 360^\circ \] \[ = 93.6^\circ \]

Step 3: Verify the result. Since Store S accounts for \(26\%\) of the total sales, its share should be slightly more than one-fourth of the full circle. One-fourth of a circle is: \[ \frac{360^\circ}{4} = 90^\circ \] Since \(26\%\) is slightly greater than \(25\%\), the angle should be slightly greater than \(90^\circ\). Our calculated value is: \[ 93.6^\circ \] which is perfectly reasonable.

Step 4: Select the correct option. The calculated central angle is \[ 93.6^\circ \] which matches: \[ \boxed{\text{Option (B)}} \] Conclusion: The central angle corresponding to Store S is \[ \boxed{93.6^\circ} \] Hence, the correct answer is Option (B).