Math, asked by princemaan0123, 10 months ago

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?​

Answers

Answered by haridasan85
10

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

Answered by shahegulafroz
7

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 .

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