Question

The circumference of two circles are in the ratio 2 : 3. Find the ratio of their areas.

Answer 1

Answer:

The Ratio of area of two circles is 4 : 9.

Step-by-step explanation:

SOLUTION :  

Let the circumference of two circles be C1 & C2 and radius of the two surface be r1 & r2.

Given : C1 : C2 = 2 : 3  

Circumference of a circle = 2πr  

C1 : C2 = 2 : 3  

2πr1 : 2πr2 = 2 : 3  

2πr1 / 2πr2 = 2/3  

r1/r2 = ⅔ ………….(1)

 

Let the area of two circles be A1 & A2

Area of circle = πr²

Ratio of area of two circles = πr1² : πr2²

A1 : A2 = πr1² : πr2²

A1/ A2 = πr1²/ πr2²

A1/ A2 = r1²/ r2²

A1/ A2 = (r1/r2)²

A1/ A2 = (⅔)²

[From eq. 1]

A1/ A2 = 4/9

A1 : A2 = 4:9

Hence, the Ratio of area of two circles is 4 : 9.

HOPE THIS ANSWER WILL HELP YOU...

Answer 2

Hello .

Here's your answer..

Ratio of circumference=2:3

ratio of radius=circumference/circumference=2πr/2πr

2/3=2πr/2πr

r/r=2/3=2:3

ratio of area=πr square/πr square

=4/9

=4:9

Hope it helps..

Ples mark brainliest ☺