If the area of a circle increases from 9π   to 16π,   then what will be the ratio of the circumference of the first circle to the second circle?

# If the area of a circle increases from   to   then what will be the ratio of the circumference of the first circle to the second circle?

1. A
3: 4
2. B
4: 3
3. C
2: 3
4. D
3: 2

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### Solution:

Given, the increment in the area of a circle is from   to  .
We have to find the ratio of the circumference of the first circle to the second circle.
We know that area of the circle is  .
Let for circle 1, the area of the circle is   and for circle 2, the area of the circle is  .
We get,

Also,

Now, the circumference of a circle is given by  .
Circumference of circle 1 is  .

Also,

Now, the ratio of the circumference of the first circle to the second circle is given by,

Therefore, the ratio of the circumference of the first circle to the second circle is 3: 4.
Hence, the correct option is 1.

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