If the radius of a circle is tripled, by what factor does the area increase? (20

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Question: If the radius of a circle is tripled, by what factor does the area increase? (2021)

Options:

Correct Answer: 9

Exam Year: 2021

Solution:

Area increases by a factor of (3r)²/r² = 9.

If the radius of a circle is tripled, by what factor does the area increase? (2021)

If the radius of a circle is tripled, by what factor does the area increase? (2021)

Step 1: Understand that the area of a circle is calculated using the formula A = πr², where r is the radius.
Step 2: Identify the original radius of the circle as r.
Step 3: Calculate the original area using the formula: A_original = πr².
Step 4: If the radius is tripled, the new radius becomes 3r.
Step 5: Calculate the new area using the new radius: A_new = π(3r)².
Step 6: Simplify the new area: A_new = π(9r²) = 9πr².
Step 7: Compare the new area to the original area: A_new / A_original = (9πr²) / (πr²).
Step 8: Simplify the fraction: (9πr²) / (πr²) = 9.
Step 9: Conclude that the area increases by a factor of 9.

Area of a Circle – The area of a circle is calculated using the formula A = πr², where r is the radius.
Scaling Factors – Understanding how changes in dimensions (like radius) affect derived quantities (like area) through squaring the scaling factor.