Question

11. The ratio of diameters of two circles is 5 : 6. Find the ratio of their circumferences.
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Answer 1

Answer:

5:6

Step-by-step explanation:

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Answer 2

We are given that the ratio of diameters of two circles is 5 : 6, and we need to find the ratios of their circumferences.

We Have :

$\sf{Diameter_{(Circle1)} \: : \: Diameter_{(Circle2)}\:=\: 5\::\:6}$

To Find :

$\sf{Circumference_{(Circle1)} \: : \: Circumference_{(Circle2)}\:= \: ?}$

Solution :

$\bf{Diameter_{(Circle1)} \: : \: Diameter_{(Circle2)}\:=\: 5\::\:6}$

$\longrightarrow \sf{\dfrac{Diameter_{(Circle1)}}{Diameter_{(Circle2)}} = \dfrac{5}{6}}$

We know that :

Radius (r) = D/2

$\longrightarrow \sf{\dfrac{Radius_{(Circle1)}}{Radius_{(Circle2)}} = \dfrac{\frac{5}{\cancel{2}}}{\frac{6}{\cancel{2}}}}$

$\longrightarrow \sf{\dfrac{Radius_{(Circle1)}}{Radius_{(Circle2)}} = \dfrac{5}{6}}$

Let the common factor between their ratios be x

$\longrightarrow$ Radius of Circle 1 = 5x

$\longrightarrow$ Radius of Circle 2 = 6x

Using Formula : Circumference of Circle = 2πr

Circumference of Circle 1

$\longrightarrow$ 2πr1

$\longrightarrow$ 2π × 5x

Circumference of Circle 2

$\longrightarrow$ 2πr2

$\longrightarrow$ 2π × 6x

$\bf{\dfrac{Circumference_{(Circle1)}}{Circumference_{(Circle2)}}\:= \: \dfrac{\cancel{2 \pi} \times 5\cancel{x}}{\cancel{2 \pi} \times 6\cancel{x}}}$

$\sf{\dfrac{Circumference_{(Circle1)}}{Circumference_{(Circle2)}}\:= \: \dfrac{5}{6}}$

$\sf{Circumference_{(Circle1)} \: : \: Circumference_{(Circle2)}\:= \: 5 \: : \: 6$