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Alexandria Dodd

Answered question

2022-03-03

Find the similarity ratio of two circles with areas

75 π c m^{2} and 27 π c m^{2}

Lana Barlow

Beginner2022-03-04Added 4 answers

Area of the first circle,

A_{1} = 75 π c m^{2}

Area of the second circle,

A_{2} = 27 π c m^{2}

Let the radius of the circles be

r_{1} and r_{2}

respectively.

A_{1} : A_{2} = 75 π : 27 π

pi cancels pi and we have both 27 and 75 divisible by 3
So, we can simplify this as

A_{1} : A_{2} = 25 : 9

....(1)
The scale (similarity) factor for circles is the ratio of the radius
Similarity factor

= r_{1} : r_{2}

Area of a circle

= π r^{2}

A_{1} : A_{2} = π r_{1}^{2} : π r_{2}^{2}

This simplifies to

A_{1} : A_{2} = r_{1}^{2} : r_{2}^{2}

.....(2)
From 1 and 2, we have

r_{1}^{2} : r_{2}^{2} = 25 : 9

Taking square root both sides we get

r_{1} : r_{2} = 5 : 3

So, the similarity ratio is 5:3 [Answer]

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