Question

If the circumference of two circles are in the ratio 2 : 3, what is the ratio of their areas?

Answer 1

Answer:

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

Step-by-step explanation:

Given :  

Circumference of two circles are in the ratio 2 : 3

Let C1 & C2  be the Circumference of two circles.

C1 : C2 = 2 : 3  

circumference of circle = 2πr  

Let the radius of the circles be r1 and r²

C1 : C2 = 2πr1 : 2πr2

2 : 3 = 2πr1 : 2πr2

⅔ = 2πr1 / 2πr2

⅔ = r1/r2 …………….(1)

Area of circle = πr²

Let A1 & A2  be the Area of two circles

Ratio of areas of two circles =  πr1²/πr2²

A1 : A2 = πr1² : πr2²

A1 / A2 = r1²/r2²

A1 / A2 = ( r1/r2)²

A1 / A2 = (2/3)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

here is the correct answer