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 day elements correspond to p%, then what is the central angle of the sector representing p on the pie diagram?

Correct Answer: The correct option is 108°.

Step-by-step Explanation:

Step 1: Understand the given distribution
In a pie diagram, the total percentage of all components equals 100%.
We are given the percentage distribution of three components in the human body:
1. Water = 70%
2. Proteins = 16%
3. Other dry elements

Step 2: Calculate the percentage of other dry elements
Let the percentage of other dry elements be E.
Since the total percentage is 100%:

$70\%+16\%+E=100\%$

$86\%+E=100\%$

$E=100\%-86\%=14\%$

Step 3: Determine the value of p%
The question states that p% corresponds to the combined percentage of both proteins and the other dry elements.
Therefore:

$p=\text{Percentage of proteins}+\text{Percentage of other dry elements}$

$p=16\%+14\%=30\%$

Step 4: Calculate the central angle representing p
The total central angle of a circle/pie chart is 360°, which corresponds to 100%.
To find the central angle corresponding to p% (which is 30%), we use the formula:

$\text{Central Angle}=\left(\frac{\text{Value of sector}}{\text{Total Value}}\right)\times 360°$

Substituting the values:

$\text{Central Angle}=\left(\frac{30}{100}\right)\times 360°$

$\text{Central Angle}=0.3\times 360°=108°$

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