Question

In a pie chart, the angle of each sector is calculated by using the formula:
$
{\rm{A.}}\,\dfrac{{{\rm{Component Part}}}}{{{\rm{Total}}}}{\rm{ \times 100}}\\
{\rm{B.}}\,\dfrac{{{\rm{Component Part}}}}{{{\rm{Total}}}}{\rm{ \times 360}}\\
{\rm{C.}}\,\dfrac{{{\rm{Component Part}}}}{{{\rm{Total}}}}{\rm{ \times \pi }}\\
{\rm{D.}}\,\dfrac{{{\rm{Total}}}}{{{\rm{Component}}\,{\rm{Part}}}}{\rm{ \times \pi }}
$

Answer 1

Hint: In this question we have to find the simple formula about how to calculate the angle subtended by each sector at center in a pie chart. For this we will use the basic understanding of fractions to derive this formula.

Complete step by step answer:
We know that in a pie chart there are different sectors of the total number of entries there are. All of the entries have some value. And all of them when added give the total sum of values. This is equivalent to the total number of entries we can say that in total number of values, every entry has a fractional value, if we try to explain with an example.

If there are 100 fruits out of which there are five categories of fruits included in them, and one of them is oranges. And the number of oranges is 25, oranges have a fraction in the total number of fruits which is equal to one fourth of the total number of fruits. It is the fraction of oranges in the total number of fruits but if we try to make a pie chart with this value, a pie chart is a circle and it has in total, 360 degrees, out of which one fourth would be oranges.

Hence the number of degrees of angle which would be of oranges in that pie chart will be:
$\dfrac{1}{4} \times 360 = {90^ \circ }$
Hands on the basis of this explanation we can say that the correct formula for angle subtended is equal to:
$\,\dfrac{{{\rm{Component Part}}}}{{{\rm{Total}}}}{\rm{ \times 360}}$
Here Component part refers to the number of values of that part, and total means the total number of values in whole.

Hence, we have established the formula and the correct option is option B.

Note:Topic such as Pie Charts are basically the topics of mathematics where the main derivations are done. If we can easily direct the charts with the shape as mentioned in the name of the charts, calculations would be very easy. Pie chart deals with circular shaped data graph whereas a bar graph shows data in the shape of rectangular or square shaped figures. Here, we used the concept that the total is 360 degrees for a pie chart as it is in circular shape.