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zaharov [31]
3 years ago
6

The ratio of the circumference of two circles is 3:2.What is the ratio of their area

Mathematics
1 answer:
Nezavi [6.7K]3 years ago
5 0

The ratio of their area is 9/4

<h2>Explanation:</h2>

We use ratios to compares values. In this exercise, we are comparing the circumference of two circles, which is:

3:2

and we want to know what is the ratio of their area. Recall that the circumference of a circle is given by:

C=2\pi r \\ \\ \\ Where: \\ \\ C:Circumference \\ \\ r:Radius \ of \ the \ circle

If we define:

C_{1}: \ Circumference \ of \ circle \ 1 \\ \\ C_{2}: \ Circumference \ of \ circle \ 2 \\ \\ r_{1}: \ Radius \ of \ circle \ 1 \\ \\ r_{2}: \ Radius \ of \ circle \ 2

Then, the ratio of the circumference of two circles is 3:2 is:

\frac{C_{1}}{C_{2}}=\frac{2\pi r_{1}}{2\pi r_{2}}=\frac{3}{2} \\ \\ \therefore \frac{r_{1}}{r_{2}}=\frac{3}{2}

The area of a circle is given by:

A=\pi r^2 \\ \\ A:Area \\ \\ r:Radius

So the ratio of their area can be found as:

\frac{A_{1}}{A_{2}}=\frac{\pi r_{1}^2}{\pi r_{2}^2} \\ \\ \\ A_{1}:Area \ of \ circle \ 1 \\ \\ A_{2}:Area \ of \ circle \ 2

So:

\frac{A_{1}}{A_{2}}=\frac{r_{1}^2}{r_{2}^2}=\left( \frac{r_{1}}{r_{2}} \right)^2 \\ \\ \frac{A_{1}}{A_{2}}=\left(\frac{3}{2}\right)^2 \\ \\ \boxed{\frac{A_{1}}{A_{2}}=\frac{9}{4}}

<h2>Learn more:</h2>

Unit rate: brainly.com/question/13771948#

#LearnWithBrainly

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Read 2 more answers
Given: AC and AE are common external tangents of G and D. BC= 123 GB=20 and AG=101. What is the measure of AC?​
Solnce55 [7]

Answer:

The length of AC is 222 units.

Step-by-step explanation:

Given AC and AE are common external tangents of G and D.

BC= 123 ,  GB=20 and AG=101.

We have to find the measure of AC.

As, a straight line joined from the center i.e radius is perpendicular to tangent drawn. Therefore,

In ΔABG, by Pythagoras theorem

AG^2=AB^2+BG^2

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⇒ AB=99 units.

Hence, AC=AB+BC=99+123=222 units.

The length of AC is 222 units.

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