Question

The ratio of two radii of two circles is 4:5.Finf the ratio of their areas

Answer 1

$\huge\underline\mathrm{Question-}$

The ratio of radii of two circles is 4:5. Find the ratio of their areas.

$\huge\underline\mathrm{Answer-}$

$\large{\boxed{\red{\rm{Ratio\:of\:areas\:of\:circles=16:25}}}}$

$\huge\underline\mathrm{Explanation-}$

Given :

• Ratio of radii of two circles = 4:5

To find :

• Ratio of areas of two circles

Formula used :

• Area of circle = πr²

Solution :

Let the radii of two circles be 4x and 5x.

$\boxed{\rm{Ratio\:of\:areas\:of\:two\:circles=\dfrac{area\:of\:1st\:circle}{Area\:of\:2nd\:circle}}}$

$\mapsto$ Ratio of areas of two circles = $\dfrac{\cancel{\pi}\:{r_1}^2}{\cancel{\pi}\:{r_2}^2}$

Putting the given values :

$\mapsto$ Ratio of areas of two circles = $\dfrac{(4x)^2}{(5x)^2}$

Solving the square, we get,

$\mapsto$ Ratio of areas of two circles = $\dfrac{16\cancel{x^2}}{25\cancel{x^2}}$

$\large{\boxed{\red{\rm{\therefore\:Ratio\:of\:areas\:of\:circles=16:25}}}}$

Answer 2

Answer:

Ratio of Areas of the Circles = 16:25

Step-by-step explanation:

We Have :-

Radius of first circle = r

Radius of second circle = r

To Find :-

Ratio of areas

Formula Used :-

Area = π r²

Solution :-

$Area\ of\ first\ circle = 3.14 * r_{1} ^{2} \\\\Area\ of\ second\ circle = 3.14 * r_{2} ^{2} \\\\\frac{Area\ of\ first\ circle}{Area\ of\ second\ circle} = \frac{3.14*r_{1}^{2} }{3.14*r_{2}^{2} }$

$=\frac{r_{1}^{2} }{r_{2}^{2} }$

$= \frac{16}{25}\\ \\Ratio\ of\ Areas = 16:25$