Discussion
The time spent by a student during a day in different activities is represented by sectors of central angles in a pie chart as given below :
School-90°
Homework-60°
Play-60°
Sleep-120°
Others-30°
What is the difference between the time spent by the student in the activities 'sleep' and 'school'?
Answer: B
The difference is 2 hours.
A pie chart for one day represents 24 hours by 360°, so each degree is 24/360 = 1/15 hour. Sleep has 120° and school 90°:
\[ \begin{aligned} &(120^{\circ} - 90^{\circ}) \times \frac{24}{360} \\ &= 30 \times \frac{1}{15} = 2 \end{aligned} \]
Sleep is 8 hours and school 6 hours. Four hours is the time for play or homework (60°), not the difference asked for; 3 hours would need a gap of 45°, and 1½ hours a gap of 22.5°.
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