10. The diameters of two circles are in the
ratio 1:3. Find the ratio of their
circumference and areas.
Answers
Here is your answer:-
Given:- The ratio of the diameters of 2 circle is 1:3
To Find:- The ratio of their circumference and areas
Solution:-
Let the diameter of the 2 circles be D1 & D2 and the circumference of the circles be C1 &C2 and also the areas of the circles be A1 & A2.
According to given condition
D1/D2=1/3
We know that,
Circumference of circle=2πR
= πD -------{R=D/2}
∴C1/C2=πD1/πD2
C1/C2= D1/D2
C1/C2= 1/3
∴C1:C2=1:3
Also area of the circle = πR²
= π(D/2)²
∴A1/A2=[π(D1/2)²]/[π(D2/2)²]
A1/A2=[D1/D2]² -------{π, π get canceled and 2², 2² also got canceled}
A1/A2=[1/3]²
A1/A2=1/9
∴A1:A2=1:9
Hence the ratio of their circumference is 1:3 and the ratio of their areas is 1:9
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