A pie diagram shows the percentage distribution of proteins, water and other dry elements in the human body. Given that proteins correspond to 16%…

Correct Option

The problem provides the percentage distribution of components in the human body:

• Percentage of proteins = 16%
• Percentage of water = 70%

To determine the percentage of other dry elements, subtract the known percentages from the total (100%):

Percentage of other dry elements = $100\% - (16\% + 70\%)$100%−(16%+70%) = $100\% - 86\%$100%−86% = $14\%$14%

The variable 'p' represents the combined percentage of proteins and other dry elements:

p% = Percentage of proteins + Percentage of other dry elements = $16\% + 14\%$16%+14% = $30\%$30%

In a pie diagram, the total central angle is 360°. Therefore, 1% corresponds to $\frac{360^\circ}{100}$100360∘​ = $3.6^\circ$3.6∘.

The central angle for p% (30%) is calculated as:

Central angle = $30 \times 3.6^\circ$30×3.6∘ = $108^\circ$108∘

Thus, the central angle of the sector representing p on the pie diagram is 108°.

Incorrect Options

The calculated central angle for p% (30%) is 108°. The other options do not correspond to this value.

• Option 1 (54°): This angle would represent $\frac{54^\circ}{3.6^\circ/\%}$3.6∘/%54∘​ = 15%. This does not match the calculated p% (30%).
• Option 2 (96°): This angle would represent $\frac{96^\circ}{3.6^\circ/\%}$3.6∘/%96∘​ $\approx$≈ 26.67%. This does not match the calculated p% (30%).
• Option 4 (120°): This angle would represent $\frac{120^\circ}{3.6^\circ/\%}$3.6∘/%120∘​ $\approx$≈ 33.33%. This does not match the calculated p% (30%).

Therefore, options 1, 2, and 4 are incorrect as they do not represent the central angle corresponding to p%.