How to Determine the Order of Sectors by Area

Question:

Zach, Adam, and Carlos are working on an art project. Sort the three sectors in order of increasing area. Place the sector with the smallest area on top.

a. Zach, Carlos, Adam
b. Carlos, Zach, Adam
c. Zach, Adam, Carlos
d. Adam, Zach, Carlos

Answer:

Without information on the size of each sector for Zach, Adam, and Carlos, it is impossible to sort them by area.

Explanation: To sort the sectors Zach, Adam, and Carlos by increasing area, you will need more information about the size of each sector. Without additional context, such as the radii of the sectors or the angle of the sectors, it is impossible to definitively sort Zach, Adam, and Carlos by area. Since we lack this crucial information, we cannot accurately determine the order.

The provided options for comparison of the areas A₁, A₂, and A3 (given as a. A₁ A₂ A3, b. A₁ = A₂ = A3, c. A₁ = A₂ > A3, d. A₁ > A₂ = A3) suggest different relationships between the areas of the sectors but, again, without specific measurements or values, these cannot be evaluated for correctness. As such, no valid answer can be given to either set of instructions (related to Zach, Adam, Carlos, or A₁, A₂, A3) without further data.

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