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16 Sep 2014, 01:08
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What will be the percentage increase in the area of a circle if the circumference of the circle increases by 10%? (The area of a circle is calculated using the formula: \(area = \pi r^2\), where \(r\) is the radius. The circumference of a circle is calculated with the formula: \(circumference = 2\pi r\).)
A. 20%
B. 21%
C. 36%
D. 40%
E. 44%
A. 20%
B. 21%
C. 36%
D. 40%
E. 44%
16 Sep 2014, 01:08
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Official Solution:
What will be the percentage increase in the area of a circle if the circumference of the circle increases by 10%? (The area of a circle is calculated using the formula: \(area = \pi r^2\), where \(r\) is the radius. The circumference of a circle is calculated with the formula: \(circumference = 2\pi r\).)
A. 20%
B. 21%
C. 36%
D. 40%
E. 44%
The circumference of the circle increases by 10%" implies that the radius of the circle also increases by 10%. The new area becomes \(\pi(1.1r)^2 = 1.21\pi r^2\). Hence, the area increases by 21%.
Answer: B
What will be the percentage increase in the area of a circle if the circumference of the circle increases by 10%? (The area of a circle is calculated using the formula: \(area = \pi r^2\), where \(r\) is the radius. The circumference of a circle is calculated with the formula: \(circumference = 2\pi r\).)
A. 20%
B. 21%
C. 36%
D. 40%
E. 44%
The circumference of the circle increases by 10%" implies that the radius of the circle also increases by 10%. The new area becomes \(\pi(1.1r)^2 = 1.21\pi r^2\). Hence, the area increases by 21%.
Answer: B
22 Oct 2023, 13:50
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I've revised the question and solution, incorporating additional details for improved clarity. I trust this makes it more comprehensible.
