Question

the ratio of the perimetre of circle A to the perimetre of the circle B is 3:1 what is the ratio of the area of the circle A to the area of circle B​

Answer 1

Step-by-step explanation:

The formula for the perimeter of a circle is 2*pi*r where r is the radius of the circle and pi is 3.14……

Assume that the perimeter of circle A is 2*pi*r(a) and that of circle B is 2*pi*r(b).

As per the question, (2*pi*r(a))/(2*pi*r(b))= 3/1

That gives us r(a)/r(b) = 3.

Now the area of a circle is pi*r*r.

So we can square the radii relation to give (r(a)/r(b))^2 = 9/1

Multiplying the numerator and denominator by pi and splitting the square will give us,

pi*(r(a))^2/(pi*r(b))^2)=9/1.

Coincidentally, the numerator of the above equation is the area of circle A and the denominator is the area of circle B.

Hence, the ratio of the area of circles is 9:1.

Answer 2

Answer:

the ratio of their areas is 9:1

Step-by-step explanation:

Perimeter of a circle =2π r

perimeter of A /perimeter of B = 3/1

Perimeter of circle A =3*perimeter of circle B

2π R =,3*2π r

R=3 r

Area of circle =π r²

Their area ,

.πR²/πr²

=π (3r) ²/πr²

=9r²/r²

=9:1