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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
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Practice Questions
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Q1
If a circle's radius is tripled, how does its area change? (2023) 2023
Increases by 3 times
Increases by 6 times
Increases by 9 times
Remains the same
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Area = πr². If radius is tripled, new area = π(3r)² = 9πr², which is 9 times the original area.
Questions & Step-by-step Solutions
1 item
Q
Q: If a circle's radius is tripled, how does its area change? (2023) 2023
Solution:
Area = πr². If radius is tripled, new area = π(3r)² = 9πr², which is 9 times the original area.
Steps: 7
Show Steps
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.
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