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If the radius of a circle is doubled, how does the area change? (2021)
If the radius of a circle is doubled, how does the area change? (2021)
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Practice Questions
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Q1
If the radius of a circle is doubled, how does the area change? (2021)
It doubles
It triples
It quadruples
It remains the same
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Area = πr²; if r is doubled, area = π(2r)² = 4πr², so it quadruples.
Questions & Step-by-step Solutions
1 item
Q
Q: If the radius of a circle is doubled, how does the area change? (2021)
Solution:
Area = πr²; if r is doubled, area = π(2r)² = 4πr², so it quadruples.
Steps: 8
Show Steps
Step 1: Understand the formula for the area of a circle, which is Area = πr², where r is the radius.
Step 2: If the radius is doubled, we replace r with 2r in the formula.
Step 3: Substitute 2r into the area formula: Area = π(2r)².
Step 4: Calculate (2r)², which is 4r².
Step 5: Now the area formula becomes Area = π(4r²).
Step 6: Simplify the area formula to Area = 4πr².
Step 7: Compare the new area (4πr²) to the original area (πr²).
Step 8: Notice that the new area is 4 times the original area, meaning it quadruples.
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