What is the relationship between the radius and the area of a circle? (2022)

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Question: What is the relationship between the radius and the area of a circle? (2022)

Options:

Correct Answer: Area is proportional to the square of the radius.

Exam Year: 2022

Solution:

The area of a circle is given by A = πr², indicating that area is proportional to the square of the radius.

What is the relationship between the radius and the area of a circle? (2022)

What is the relationship between the radius and the area of a circle? (2022)

Step 1: Understand that a circle has a center point and all points on the edge are the same distance from this center. This distance is called the radius (r).
Step 2: The area of a circle is the space inside it. We use a special formula to calculate this area.
Step 3: The formula for the area (A) of a circle is A = πr², where π (pi) is a constant approximately equal to 3.14.
Step 4: In the formula A = πr², notice that the radius (r) is squared (r times r). This means if you double the radius, the area increases by four times.
Step 5: Therefore, the area of a circle grows faster than the radius. If the radius gets bigger, the area gets much bigger.

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