Question

$\begin{array}{cc}\text{Season}& \text{No. of votes}\\ \text{Summer}& \text{90}\\ \text{Rainy}& \text{120}\\ \text{Winter}& \text{150}\end{array}$

A group of 360 people were asked to vote for their favourite season from the three seasons: rainy, winter and summer. Find the central angle of each sector in a pie chart for the above information. [4 MARKS]

Answer 1

Formula: 1 Mark
Application: 1 Mark each

Central Angle can be calculated as follows:

$\frac{\text{Season's Number of Votes}}{\text{Total Votes}}\times {360}^{\circ }$

Summer's Central Angle $=\frac{90}{360}\times {360}^{\circ }={90}^{\circ }$

Rainy's Central Angle $=\frac{120}{360}\times {360}^{\circ }={120}^{\circ }$

Winter's Central Angle $=\frac{150}{360}\times {360}^{\circ }={150}^{\circ }$