Question

A group of pupils of a certain school named the subject they liked most. Their
choices are represented on the given pie chart.
Show that the value of x is 32
(a
(b) Calculate the percentage of the group who like science.
(c) Given that 48 pupils chose Mathematics, calculate the total number of pupils in
the group​

Answer 1

Given : A group of pupils of a certain school named the subject they liked most. Their choices are represented on the given pie chart.

Given that 48 pupils chose Mathematics

To Find : Show that the value of x is 32

Calculate the percentage of the group who like science.

calculate the total number of pupils in the group​

Solution:

A pie chart (or a circle chart) is a circular statistical graphic, which is divided into slices to illustrate numerical proportion.

In a pie chart, the arc length of each slice (and consequently its central angle and area), is directly proportional to the quantity it represents.

In a pie chart, each sector represents a particular part of data  

and  the magnitude of the sector is directly proportional to the magnitude of the specific part of the data

Total angle at center = 360°

=> 2x° + 55° + 5x° + 81°  = 360°

=> 7x° + 136° = 360°

=> 7x°  = 224°

=> x° = 32°

=>  x= 32

percentage of the group who like science.

= (81°/360°) * 100

= 81  * 10 /36

= 9 * 10 / 4

= 9 * 5 / 2

= 45/2

= 22.5 %

5x = 5(32) = 160°

160°  represent 48

=>  total number of pupils in the group​  = (48 / 160° ) * 360° = 108

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