Question

The radii of two circle are in the ratio 2:3 what is the ratio of their circumfrences

Answer 1

Answer:

Given :-

• The radii of two circle are in the ratio of 2:3.

To Find :-

• What is the ratio of their circumference.

Formula Used :-

We know that,

$\sf\boxed{\bold{\large{Circumference\: of\: circle\: =\: 2{\pi}r}}}$

Solution :-

$\mapsto$ Let, the first radius be 2x

$\mapsto$ And, the second radius be 3x

Now, circumference of a first circle,

⇒ $\sf 2 \times \dfrac{22}{7} \times 2x$

⇒ $\sf 2 \times 2x \times \dfrac{22}{7}$

➠ $\sf\bold{4x \times \dfrac{22}{7}}$

Again, circumference of a second circle,

↦ $\sf 2 \times \dfrac{22}{7} \times 3x$

↦ $\sf 2 \times 3x \times \dfrac{22}{7}$

➦ $\sf\bold{6x \times \dfrac{22}{7}}$

Now, we have to find the ratio of the circumference of two circles,

↪ $\sf\dfrac{4x \times \dfrac{22}{7}}{6x \times \dfrac{22}{7}}$

↪ $\sf\dfrac{4x}{6x}$

↪ $\sf\dfrac{\cancel{4x}}{\cancel{6x}}$

↪ $\sf\dfrac{\cancel{4}}{\cancel{6}}$

➤ $\sf\red{\dfrac{2}{3}}$

Hence, the ratio two circumference of a circle is 2:3

$\therefore$ The ratio of their circumference is 2 : 3 .

Answer 2

Given

Radii of two circles are in the ratio 2:3

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To Find

The ratio of their circumferences.

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Solution

Let's consider the radius of the two circles as 2x and 3x (Since they are in the ratio of 3:2)

We know that circumference is the perimeter of the circle. So the formula to find the circumference of a circle is ⇒ 2πr

Here 'r' is the radius and 'π' is the pi.

Circle 1

Circumference ⇒ 2πr

Radius ⇒ 2x

Circumference ⇒ 2π(2x)

Circumference ⇒ $2\times \dfrac{22}{7}\times 2x$

Circumference ⇒ $\dfrac{44}{7}\times 2x$

Circumference ⇒ $\dfrac{88}{7}x$

∴ The circumference of Circle 1 is $\bf \dfrac{88}{7}x$

Circle 2

Circumference ⇒ 2πr

Radius ⇒ 3x

Circumference ⇒ 2π(3x)

Circumference ⇒ $2\times \dfrac{22}{7}\times 3x$

Circumference ⇒ $\dfrac{44}{7}\times 3x$

Circumference ⇒ $\dfrac{132}{7}x$

∴ The circumference of Circle 2 is $\bf \dfrac{132}{7} x$

The ratio of the two circumferences ⇒ $\dfrac{\frac{88}{7}x }{\frac{132}{7} x}$

⇒ $\dfrac{88}{7}x \div \dfrac{132}{7}x$

⇒ $\dfrac{88}{7}x \times \dfrac{7}{132}x$

⇒ $\dfrac{88x}{132x}$

⇒ $\dfrac{88x\div 4 4}{132x\div 44 }$

⇒ $\dfrac{2}{3}$

⇒ $2:3$

∴ The ratio of their circumferences is 2:3

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