Question

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

Answer 1

Answer:

P1: P2 = 3:1

2πr 1:2πr 2= 3:l

ri: r2=3:l

A1: A2 = πr 1^2:πr 2^2

= π3^2:πI^2

= 9:1

ratio of areas=9:1

Answer 2

Answer:

The ratio of the  area of circle A to the area of circle B 9:1 .

Step-by-step explanation:

Given -

The ratio of the perimeter of circle A to the perimeter of circle B is 3:1.

To find -

The ratio of the  area of circle A to the area of circle B

Solution -

As we know that,

Perimeter of circle = $2\:\pi \:r$

Where,

r = radius of circle

let , the perimeter of circle A is 3x having radius $r_{1}$ and the  the perimeter of circle B is 1x having radius $r_{2}$

So, we can write given information as,

$\frac{perimeter of circle A}{perimeter of circle B} =\frac{2\:\pi \:r_{1} }{2\:\pi \:r_{2} }$

Put the given values,

$\frac{3x}{1x} =\frac{2\:\pi \:r_{1} }{2\:\pi \:r_{2} }$

As 2 π is present numerator as well as denominator it get cancel .

$\frac{3x}{1x} =\frac{r_{1} }{r_{2} }$

As $x$ is present numerator as well as denominator it get cancel .

$\frac{3}{1} =\frac{r_{1} }{r_{2} }$

$r_{1} = 3\:cm \:and\: r_{2} = 1\:cm$

∴ Ration of radius of circle A is to B is $\frac{3}{1}$

Area of a circle = $\pi r^{2}$

By taking ration π get cancel .

So, we can say that

Area of circle is directly proportional to the square radius of a circle.

$\frac{Area\: of \:circle \:A}{Area\: of \:circle \:B} =\frac{r_{1}^{2} }{r_{2}^{2} }$

$\frac{Area\: of \:circle \:A}{Area\: of \:circle \:B} =\frac{3^{2} }{1^{2} }$

$\frac{Area\: of \:circle \:A}{Area\: of \:circle \:B} =\frac{9 }{1 }$

∴ The ratio of the  area of circle A to the area of circle B 9:1 .