Question

the circumference of two circles are in the ratio 4:7. find the ratio of their areas.​

Answer 1

Given,

The circumference of two circles are in the ratio 4:7.

To find out,

Find the ratio of their areas.

Solution:

We know that circumference of circle = 2πr

Let us take the radius of first circle be r1 and radius of second circle be r2.

Now, as it is given the ratio is 4/7.

Then,

$\frac{2 \: \pi \: r1}{2 \: \pi \: r2} = \frac{4}{7} \\ \\ \frac{r1}{r2} = \frac{4}{7}$

According to the problem,

$area \: of \: circle \: = 2 \pi \: {r}^{2}$

$\frac{area \: of \: first \: circle}{area \: of \: second \: circle} = \frac{2 \pi \: {(r1)}^{2} }{2 \pi \: {(r2)}^{2} }$

$\frac{ {(r1)}^{2} }{ {(r2)}^{2} } = \frac{ {4}^{2} }{ {7}^{2} } \\ \\ \frac{ {(r1)}^{2} }{ {(r2)}^{2} } \: = \frac{16}{49}$

Therefore the ratio of area of circles is 16:49.