Question

The teacher decides to show the data in the circle graph (pie chart). What should be the measure of the central angle of the sector for 3 hours?
A. 18
B. 20
C. 36
D. 72
E. 90

Answer 1

Hint: In this question, we are given that the teacher is showing the data regarding the number of hours in the clock in the form of a circle chart or a pie chart. We know that there are a total 12 hours in the clock which is shown by ${360^ \circ }$ of the pie chart. By keeping this in mind, we will determine the center of the sector for 3 hours.

Complete step by step answer:
We know that the whole pie chat of ${360^ \circ }$ will show the total of 12 hours of the clock.
Now, to find out the central angle of the sector for 3 hours. We will use the following method.
Let us consider that the central angle of the sector for 3 hours is ${x^ \circ }$.

Hours	Angle ( degree $^ \circ $)
12	360
3	$x$

Therefore we can say that $x = \dfrac{{3 \times 360}}{{12}} = 90$.
Thus, the value of the central angle of the sector for 3 hours is ${90^ \circ }$.

Hence, option E is the right answer.

Note: We can also solve this problem by using another method.
We know that 3 hours is the fourth part of 12 hours.
Therefore, we can say that the central angle of the sector for 3 hours is one fourth of the total angle and total angle is ${360^ \circ }$.
Therefore, the central angle of the sector for 3 hours $ = \dfrac{1}{4} \times {360^ \circ } = {90^ \circ }$.