Question

if the ratio of the area of two circles is 16 : 25 then what is the radius of the two circles?​

Answer 1

GIVEN :–

• The ratio of the area of two circles is 16:25 .

TO FIND :–

• Ratio of radius of the two circles = ?

SOLUTION :–

• We known that –

$\\ \red \implies{ \large \pink{\boxed{\bf Area \: \: of \: \: circle = \pi {r}^{2}}}}$

• Let the radius of circles are r₁ & r₂ respectively.

$\\\implies\bf \dfrac{A_1}{A_2}= \dfrac{ \pi {r_1}^{2}}{\pi {r_2}^{2}}$

$\\\implies\bf \dfrac{A_1}{A_2}= \dfrac{{r_1}^{2}}{{r_2}^{2}}$

• According to the question –

$\\\implies\bf \dfrac{A_1}{A_2}= \dfrac{16}{25}$

• So that –

$\\\implies\bf\dfrac{{r_1}^{2}}{{r_2}^{2}}= \dfrac{16}{25}$

• Let's take square root on both sides –

$\\\implies\bf \sqrt\dfrac{{r_1}^{2}}{{r_2}^{2}}= \sqrt\dfrac{16}{25}$

$\\\implies\bf\dfrac{r_1}{r_2}= \sqrt\dfrac{16}{25}$

$\\\implies \large\boxed{\bf\dfrac{r_1}{r_2}= \dfrac{4}{5}}$

• Hence , The value of r₁ : r₂ = 4 : 5.

Answer 2

Question :

if the ratio of the area of two circles is 16 : 25 then what is the radius of the two circles?

To find :

the radius of two circles

Formula Used :

Area of Circle = πr²

Solution :

According to the question,

Let the radius of one circle be R

Radius of another another circle be r

R and r are specified because for better identification.

Using the formula of Area of the Circle = πr² we get

$\sf \leadsto \frac{ Area_{1}}{Area_{2} } = \frac{πR²}{πr²}$

By putting the values of R and r we get

$\sf \leadsto \frac{Area_{1}}{Area_{2}} = \frac{ \pi {(4)}^{2} }{ \pi {(5)}^{2} }$

π will get cancelled

$\sf \leadsto \frac{Area_{1}}{Area_{2}} = \frac{ \cancel \pi16}{ \cancel \pi25}$

As we know,

$\sf \leadsto \frac{ {(R)}^{2} }{ {(r)}^{2} } = \frac{16}{25}$

By taking the square root on both the sides we get

$\sf \leadsto \sqrt{ \frac{ {(R)}^{2} }{ {(r)}^{2} } } = \sqrt{ \frac{16}{25} }$

Now,

$\sf \leadsto\frac{R}{r} = \frac{4}{5}$

So R is 4 and r is 5

∴ The ratio is 4 : 5