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The radius of a circle is increased by 1%. Find how much % does its area increases?
- a)1.01%
- b)5.01%
- c)3.01%
- d)2.01%
Correct answer is option 'D'. Can you explain this answer?
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The radius of a circle is increased by 1%. Find how much % does its ar...
Understanding the Problem
When the radius of a circle is increased by 1%, we need to determine the percentage increase in the area of the circle.
Area of a Circle
- The formula for the area (A) of a circle is given by:
A = πr², where r is the radius.
Calculating the New Radius
- If the original radius is r, after a 1% increase, the new radius (r') can be calculated as:
r' = r + 0.01r = 1.01r.
Calculating the New Area
- The new area (A') with the new radius can be found using:
A' = π(r')² = π(1.01r)² = π(1.0201r²).
Finding the Percentage Increase in Area
- The original area (A) is:
A = πr².
- The new area (A') becomes:
A' = π(1.0201r²) = 1.0201A.
- To find the percentage increase in the area:
Percentage Increase = [(A' - A) / A] × 100
= [(1.0201A - A) / A] × 100
= (0.0201) × 100 ≈ 2.01%.
Conclusion
- Therefore, the area of the circle increases by approximately 2.01% when the radius is increased by 1%.
- The correct answer is option 'D'.
When the radius of a circle is increased by 1%, we need to determine the percentage increase in the area of the circle.
Area of a Circle
- The formula for the area (A) of a circle is given by:
A = πr², where r is the radius.
Calculating the New Radius
- If the original radius is r, after a 1% increase, the new radius (r') can be calculated as:
r' = r + 0.01r = 1.01r.
Calculating the New Area
- The new area (A') with the new radius can be found using:
A' = π(r')² = π(1.01r)² = π(1.0201r²).
Finding the Percentage Increase in Area
- The original area (A) is:
A = πr².
- The new area (A') becomes:
A' = π(1.0201r²) = 1.0201A.
- To find the percentage increase in the area:
Percentage Increase = [(A' - A) / A] × 100
= [(1.0201A - A) / A] × 100
= (0.0201) × 100 ≈ 2.01%.
Conclusion
- Therefore, the area of the circle increases by approximately 2.01% when the radius is increased by 1%.
- The correct answer is option 'D'.
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The radius of a circle is increased by 1%. Find how much % does its area increases?a)1.01%b)5.01%c)3.01%d)2.01%Correct answer is option 'D'. Can you explain this answer?
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