If a circle's radius is tripled, how does its area change? (2023) 2023

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Question: If a circle\'s radius is tripled, how does its area change? (2023) 2023

Options:

Correct Answer: Increases by 9 times

Exam Year: 2023

Solution:

Area = πr². If radius is tripled, new area = π(3r)² = 9πr², which is 9 times the original area.

If a circle's radius is tripled, how does its area change? (2023) 2023

If a circle's radius is tripled, how does its area change? (2023) 2023

Step 1: Understand the formula for the area of a circle, which is Area = πr², where r is the radius.
Step 2: Identify the original radius of the circle as 'r'.
Step 3: If the radius is tripled, the new radius becomes 3r.
Step 4: Substitute the new radius into the area formula: Area = π(3r)².
Step 5: Calculate (3r)², which equals 9r².
Step 6: Now, substitute this back into the area formula: Area = π(9r²).
Step 7: This simplifies to Area = 9πr², which shows that the new area is 9 times the original area.

Area of a Circle – Understanding the formula for the area of a circle (A = πr²) and how changes in the radius affect the area.
Scaling Effects – Recognizing how scaling the radius by a factor affects the area, specifically that area scales with the square of the radius.