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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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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? for Interview Preparation 2024 is part of Interview Preparation preparation. The Question and answers have been prepared according to the Interview Preparation exam syllabus. Information about 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? covers all topics & solutions for Interview Preparation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 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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