We have an answer to "The ratio of the areas of two circles..."

High School
Geometry
High school geometry
Circles

embeucadaoo8

Answered question

2022-03-01

The ratio of the areas of two circles is equal to the ratio of their radii.
True or false?

Answer & Explanation

Jett Brooks

Beginner2022-03-02Added 7 answers

Step 1
According to given,
Let the radius of circle 1 be

r_{1}

.
The radius of circle 2 be

r_{2}

.
Therefore,
Area of circle 1

(A 1) = π {(r_{1})}^{2}

Area of circle 2

(A 2) = π {(r_{2})}^{2}

Step 2
Hence,
The ratio of the areas of two circles

= \frac{A_{1}}{A_{2}}

\frac{A_{1}}{A_{2}} = \frac{π {(r_{1})}^{2}}{π {(r_{2})}^{2}}

Therefore,

\frac{A_{1}}{A_{2}} = \frac{{(r_{1})}^{2}}{{(r_{2})}^{2}}

We can conclude that,
Ratio of the areas of two circles is equal to the ratio of square their radii.
Step 3
Therefore,
The statement - 'The ratio of the areas of two circles is equal to the ratio of their radii.'- is False statement.

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