If a circle's radius is tripled, by what factor does the area increase? (2019)

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Question: If a circle\'s radius is tripled, by what factor does the area increase? (2019)

Options:

Correct Answer: 9

Exam Year: 2019

Solution:

Area = πr²; If r is tripled, new area = π(3r)² = 9πr²; Factor = 9.

If a circle's radius is tripled, by what factor does the area increase? (2019)

If a circle's radius is tripled, by what factor does the area increase? (2019)

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) = 9πr².
Step 7: Compare the new area (9πr²) to the original area (πr²).
Step 8: To find the factor of increase, divide the new area by the original area: (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 Effects – Understanding how changes in the radius affect the area, specifically that area scales with the square of the radius.