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Question
The ratio between the radius of two circles is 5 : 7. Find the ratio between their:
(i) circumference
(ii) areas
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Solution
(i) The ratio of the radius of the circles = 5 : 7
Let radius of first circle = 5x
and radius of second circle = 7x
∴ Circumference of first circle = 2πr
= 2π × 5x = 10πx
and circumference of second circle
= 2π × 7x = 14πx
∴ Ratio between their circumference
= 10πx : 14πx
= 10 : 14 = 5 : 7
(ii) Area of first circle = πr2
= `22/7xx5"x"xx5"x"=550/7"x"^2`
and area of second circle = πr2
= `22/7xx7"x"xx7"x"=1078/7"x"^2`
Ratio between their areas
= `550/7"x"^2:1078/7"x"^2`
= 550 : 1078 ............(Dividing by 22)
= 25 : 49
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