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Question

If the circumference of a circle increases from 4π to 8π, then its area is :

A
Halved
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B
Doubled
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C
Tripled
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D
Quadrupled
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Solution

The correct option is C Quadrupled
Let C1, r1, A1 be the circumference, radius and area of circle with circumference as 4π
Let C2, r2, A2 be the circumference, radius and area of circle with circumference as 8π
Given,
C1=4π and ,C2=8π
C1C2=4π8π
2πr12πr2=48
r1r2=12
Now,
A1A2=πr12πr22
=>A1A2=(12)2
A1A2=14
A2=4A1
Area will be quadrupled.

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