Question

The ratio between the radii of 2 circles is 4:9. Find the ratio between their areas.

Answer 1

Answer:

1 / 5 or 1:5

Step-by-step explanation:

According to the information provided in the question it is given as

The ratio between the radii of 2 circles is 4:9.

We need to find the ratio between their areas.

The ratio between radius =  4:9

Hence

                     Radius 1st  = 4

                     Radius 2nd = 9

Area of 1st circle  [tex]= \pi r^{2} \\\\ = \frac{22}{7}\times 4^{2}\\ = 3.142 \times 4\times 4\\ = 50.272\\ [/tex]

Area of 2nd  circle = $\pi r^{2}$

Area of 2nd circle   [tex]=3.142\times 9\times 9\\ = 254.502\\ [/tex]

 Ratio  between Areas = 50.272 / 254.502

                                      = 1 / 5

             Ratio = 1 / 5 Or  1:5

Answer 2

$\large{ \bf{ \underline{Solution :}}}$

Let the radii of the two circles be r and R, the circumferences of the circles be c and C and the areas of the two circles be a and A.

Now,

$\frac{a}{A } = \frac{4}{9}$

$\space$

$\implies \: \frac{\pi \: r ^{2} }{\pi \: R ^{2} } = ( \frac{2}{3} ) ^{2}$

$\space$

$\implies \: \frac{r}{R} = \frac{2}{3}$

Now, the ratio between their circumferences is given by

$\frac{c}{C} = \frac{2\pi \: r }{\pi \: R ^{2} }$

$\space$

$\implies \: \frac{r}{R}$

$\space$

$\bold{\implies \: \frac{2}{3} }$

Hence, the ratio between their circumference is 2:3

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