The circumference of two circles are 12\pi and 36\pi. Find

Question

The circumference of two circles are

12 π

and

36 π

. Find the ratio of the areas of the circles.
a)

1 : 3

b)

1 : 9

c)

3 : 4

d)

2 : 5

Answer 1

Step 1
We know that circumference of circle

= 2 π r

For first circle

2 π r = 12 π

\Rightarrow r = 6

For second circle,

2 π r = 36 π

\Rightarrow r = 18

Step 2
Area of the circle

= π r^{2}

For first circle
Area

= π \times {(6)}^{2} [∵ r = 6]

= 36 π

For second circle
Area

= π \times {(18)}^{2} [r = 18]

= 324 π

Ratio of the area of circle is

36 π : 324 π

= 1 : 9

Itence the answe is

1 : 9

Expert Answer