Question

If the ratio of the two radii of two circles is 2:3, then the ratio of their circumference is

1 point

2:3

3:2

4:9

9:4

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Answer 1

Answer:

Let the radius of two circle be 2x and 3x respectively. Ratio of Circumference of two circles ; Hence, ratio of their Circumferences is

2:3.

Answer 2

Answer:

Answer:

$\fbox \red {THE RATIO OF THERE CIRCUMFERENCE IS 2:3 }$

Step-by-step explanation:

LET THE RADIUS OF THE TWO CIRCLE BE 2x and 3x RESPECTIVELY.

WE KNOW THAT

CIRCUMFERENCE OF CIRCLE = 2πR

LET'S FIND THE CIRCUMFERENCE OF 1ST CIRCLE:-

circumference of circle of radius 2x cm = 2πr

$\begin{gathered} = 2 \pi \: r \\ \\ = 2 \times \frac{22}{7} \times 2x \\ \\ = \frac{88x}{7} \end{gathered} </p><p>=2πr</p><p>=2× </p><p>7</p><p>22</p><p> </p><p> ×2x</p><p>= </p><p>7</p><p>88x$

SIMILARLY,

circumference of circle of radius 3x cm = 2πr

$\begin{gathered} = 2\pi \times r \\ \\ = 2 \times \frac{22}{7} \times 3x \\ \\ = \frac{132x}{7} \end{gathered} </p><p>=2π×r</p><p>=2× </p><p>7</p><p>22</p><p> </p><p> ×3x</p><p>= </p><p>7</p><p>132x$

___________________________

NOW THE RATIO OF THEIR CIRCUMFERENCES

$\begin{gathered}\frac{ratio \: of \: the \: circumference \: of \: 1st \: circle}{ratio \: of \: the \: circumference \: of \: 2nd\: circle} = \huge \bf \\ \\ \huge \bf = > \frac{ \frac{88x}{7} }{ \frac{132x}{7} } \huge \bf \\ \\ \huge \bf = > \frac{88x}{132x } \huge \bf \\ \\ \huge \bf = > \frac{22}{33} \huge \bf \\ \\ \huge \bf = > \frac{2}{3} \end{gathered} </p><p>ratioofthecircumferenceof2ndcircle</p><p>ratioofthecircumferenceof1stcircle$

$=</p><p>=> </p><p>7</p><p>132x</p><p> </p><p> </p><p>7</p><p>88x</p><p> </p><p> </p><p> </p><p> </p><p>=> </p><p>132x</p><p>88x</p><p> </p><p> </p><p>=> </p><p>33</p><p>22</p><p> </p><p> </p><p>=> </p><p>3</p><p>2</p><p>$

HENCE THE RATIO OF THERE CIRCUMFERENCE IS 2:3