Math, asked by sugargirl4130, 4 months ago

Question 2. pls answer. I will give 10 points​

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Answers

Answered by Vaibhav1230
1

Answer:

Correct Question -

The circumference of two circle are in the ratio 2 : 3. Find the ratio of their areas.

Given -

Ratio of their circumference = 2:3

To find -

Ratio of their areas.

Formula used -

Circumference of circle

Area of circle.

Solution -

In the question, we are provided, with the ratios of the circumference of 2 circles, and we need to find the ratio of area of those circle, for that first we will use the formula of circumference of a circle, then we will use the formula of area of circles. We will be writing 1 equation in it too.

So -

Let the circumference of 2 circles be c1 and c2

According to question -

c1 : c2

Circumference of circle = 2πr

where -

π = \tt\dfrac{22}{7}

r = radius

On substituting the values -

c1 : c2 = 2 : 3

2πr1 : 2πr2 = 2 : 3

\tt\dfrac{2\pi\:r\:1}{2\pi\:r\:2} = \tt\dfrac{2}{3}

\tt\dfrac{r1}{r2} = \tt\dfrac{2}{3}\longrightarrow [Equation 1]

Now -

Let the areas of both the circles be A1 and A2

Area of circle = πr²

So -

Area of both circles = πr1² : πr2²

On substituting the values -

A1 : A2 = πr1² : πr2²

\tt\dfrac{A1}{A2} = \tt\dfrac{(\pi\:r1)}{(\pi\:r2)}^{2}

\tt\dfrac{A1}{A2} = \tt\dfrac{(r1)}{(r2)}^{2}

\tt\dfrac{A1}{A2} = \tt\dfrac{(2)}{(3)}^{2} [From equation 1]

So -

\tt\dfrac{A1}{A2} = \tt\dfrac{4}{9}

\therefore The ratio of their areas is 4 : 9

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