Find the similarity ratio of two circles with areas 75 pi cm^2 and 27 pi cm^2.

ruigE 2021-02-21 Answered
Find the similarity ratio of two circles with areas 75πcm2and27πcm2.
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Expert Answer

sovienesY
Answered 2021-02-22 Author has 89 answers
Step 1: Note down the given information
Area of the first circle, A1=75πcm2
Area of the second circle, A2=27πcm2
Let the radius of the circles be r1andr2 respectively.
Step 2: Calculate the ratio of areas of the the two circles
A1:A2=75π:27π
π cancels pi and we have both 27 and 75 divisible by 3
So, we can simplify this as
A1:A2=25:9 ....(1)
Step 3: Calculate the ratio of areas in terms of r1andr2
The scale (similarity) factor for circles is the ratio of the radius
Similarity factor = r1:r2
Area of a circle = πr2
so A1:A2=πr12:πr22
This simplifies to
A1:A2=r12:r22 .....(2)
Step 4: Use equation 1 and 2 to deduce similarity ratio
From 1 and 2, we have
r12:r22=25:9
Taking square root both sides we get
r1:r2=5:3
Result: So, the similarity ratio is 5 : 3
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