Question

The ratio of the perimeter of circle A to the perimeter of circle B is 3:1. What is the ratio of thearea of circle A to the area of circle B?​

Answer 1

Perimeter of a Circle: 2(pi)r = P

P A /P B = 3/1

2(pi)r A /2(pi)r B = 3/1

r A /r B = 3/1

Area of circle: (pi)r^2 = A

A A /A B = (pi)r A ^2/(pi)r B ^2 = r A ^2/r B ^2

So, * (P A /P B )^2 = r A ^2/r B ^2 = (3/1)^2 = 9/1

Answer 2

ANSWER:

Let ratio of perimeter of circle be 3x:x

✯Perimeter of circle =2πr

$\sf \frac{perimeter \: of \:A }{perimeter \: of \:B} = \frac{3x}{x}$

$\sf \cancel \frac{2\pi \: r}{2\pi R} = \frac{3x}{x} \:$

$\sf \frac{r}{ R} = \frac{3x}{x} \:$

So radius of circle A,r=3x

Radius of circle B,R=x

Area of circle A=2π3x

Area of circle B=2πx

✯Area of circle =πr²

$\sf ratio \: of \: area = \frac{2\pi {r}^{2} }{2\pi \: {R}^{2} }$

$\sf : \implies \: \: \frac{ {3x}^{2} }{ {x}^{2} }$

$\sf : \implies \: \: \frac{ 3 }{ 1 }$

So ratio of area of circle A with B is 3:1