Question

A group of $360$ people were asked to vote for their favourite season from the three seasons rainy, winter and summer.
(i) Which season got the most votes?
(ii) Find the central angle of each sector.
(iii) Draw a pie chart to show this information

Answer 1

(i) From above table, the winter season got most votes: $150$

(ii) to calculate central angle:
We must know total votes $=90+120+150$
$=360$
By treating ${360}^{\circ }$ as an angle, all three seasons combining together, it represents a complete one revolution.
Since, number of votes for summer season $=90$ votes
$\Rightarrow$ central angle of Summer season sector is
$=\frac{90}{360}\times {360}^{\circ }$
$={90}^{\circ }$
Similar way for other two seasons,
Votes for Rainy season is $=120$ votes
$\Rightarrow$ Central angle $=\frac{120}{360}\times {360}^{\circ }$
$={120}^{\circ }$

Votes for Winter season $=150$ votes
$\Rightarrow$ Central angle $=\frac{160}{360}\times {360}^{\circ }$
$={150}^{\circ }$

(iii)