If the circumference of a circle increases from 4π to 8π .Then find increase in area.
Answers
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Answer:
If the circumference of the circle increases from 4π to 8π then the percentage increase in the area of a circle is 300%
Its area is quadrupled.
Among the given options option (d) quadrupled is the correct answer.
Step-by-step explanation:
Given :
Circumference of the circle increases from 4π to 8π.
Circumference of a circle = 2πr
Case 1 : When circumference = 4π
C = 4π
2πr = 4π
2r = 4
r = 4/2
r = 2
Radius = 2
Area of a circle,A = πr²
A = 22/7 × 2²
A = (22/7 × 4) ……. ..(1)
Case 2 : When circumference = 8π
C = 8π
2πr = 8π
2r = 8
r = 8/2
r = 4
Radius = 4
Area of a circle,A = πr²
A = 22/7 × 4²
A = 22/7 × 16
A = 4 (22/7 × 4) ……. ..(2)
From eq 1 and 2 , it is clear that area is quadrupled.
Hence, its area is quadrupled.
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