Question : The pie chart given below shows the number of students studying in six schools. Total number of students studying in all these six schools are 4000. The number of students studying in a particular school is shown as a percentage of the total number of students studying in all these six schools.
What is the difference between the central angle formed by sectors F and H together and the central angle formed by sectors I and G together?
Option 1: $9.6^{\circ}$
Option 2: $14.4^{\circ}$
Option 3: $17.4^{\circ}$
Option 4: $18.7^{\circ}$
Correct Answer: $14.4^{\circ}$
Solution :
The value of the central angle formed by the sector F $=\frac{360^{\circ}}{100}\times 16=57.6^{\circ}$
The value of the central angle formed by the sector H $=\frac{360^{\circ}}{100}\times 23=82.8^{\circ}$
The value of the central angle formed by the sector I $=\frac{360^{\circ}}{100}\times 25=90^{\circ}$
The value of the central angle formed by the sector G $=\frac{360^{\circ}}{100}\times 18=64.8^{\circ}$
The difference between the central angle formed by sectors F and H together and the central angle formed by sectors I and G together $=(90^{\circ}+64.8^{\circ})-(57.6^{\circ}+82.8^{\circ})=154.8^{\circ}-140.4^{\circ}=14.4^{\circ}$
Hence, the correct answer is $14.4^{\circ}$.
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