A pie diagram shows the percentage distribution of proteins, water and other dry elements in the human body. Given that proteins correspond to 16% and water corresponds to 70%. If both proteins and the other dry elements correspond to p%, then what is the central angle of the sector representing p on the pie diagram ?
- (a) 54°
- (b) 96°
- (c) 108° ✓ UPSC's answer
- (d) 120°
Why the answer is (c)
• The total percentage of all components in the human body is 100%.
• Water corresponds to 70% and proteins correspond to 16%.
• The percentage of 'other dry elements' is calculated as 100% - 70% - 16% = 14%.
• The problem states that both proteins and other dry elements correspond to p%, implying p is the sum of their percentages: p = 16% + 14% = 30%.
• The central angle for a sector in a pie chart is calculated as (Percentage / 100) * 360°.
• Therefore, the central angle for p (30%) is (30 / 100) * 360° = 108°.
Why the other options are wrong
- (a) 54°
- 54° corresponds to 15% of the circle, which does not match the combined 30% of proteins and other dry elements.
- (b) 96°
- 96° corresponds to approximately 26.67% of the circle, which is incorrect for the 30% total.
- (d) 120°
- 120° corresponds to 33.33% of the circle, which is higher than the actual 30% total.
Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2021, held on 10 October 2021. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.