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If a circle's radius is doubled, how does its area change? (2020)
If a circle's radius is doubled, how does its area change? (2020)
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Practice Questions
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Q1
If a circle's radius is doubled, how does its area change? (2020)
It remains the same
It doubles
It triples
It quadruples
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Area = πr². If radius is doubled (2r), new area = π(2r)² = 4πr², which is quadruple the original area.
Questions & Step-by-step Solutions
1 item
Q
Q: If a circle's radius is doubled, how does its area change? (2020)
Solution:
Area = πr². If radius is doubled (2r), new area = π(2r)² = 4πr², which is quadruple 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 what happens when the radius is doubled. If the original radius is r, the new radius becomes 2r.
Step 3: Substitute the new radius (2r) into the area formula. The new area becomes Area = π(2r)².
Step 4: Calculate (2r)². This equals 4r².
Step 5: Now substitute this back into the area formula: Area = π(4r²).
Step 6: Simplify the new area to get Area = 4πr².
Step 7: Compare the new area (4πr²) to the original area (πr²). The new area is 4 times the original area.
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