Question

the sum of the circumference of four small circles of same radius is equal to the circumference of a bigger circle find the ratio of the area of the bigger Circle to that of the smaller circle​

Answer 1

Step-by-step explanation:

Let the radius of bigger circle be R and that of smaller circles be r as radii of small circles are same.

Therefore,

$\therefore \: Circumference \: of \: bigger \: circle \\ = 4 \times \: the \: circumference \: of \: a \: \\ \: \: \: \: \: \: \: \: \: \: \: \: \: smaller \: circle \\ \implies \: 2 \pi \: R = 4 \times 2 \pi \: r \\ \implies \: 2 \pi \: R = 8 \pi \: r \\ \implies \: \frac{R}{r} = \frac{8 \pi}{2 \pi} \\ \implies \: \frac{R}{r} = \frac{4}{1} ....(1) \\ now \: \\ ratio \: of \: areas = \frac{ \pi \: {R}^{2} }{\pi \: {r}^{2}} \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \frac{{R}^{2} }{{r}^{2}} \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \frac{{4}^{2} }{{1}^{2}} \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \frac{16}{1} \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 16 : 1$

Answer 2

Four small circle having radius=r

bigger circles radius is=R

Circumference of circle is =2×π×r

4×2πr=2πR

R=4r

Area=area of bigger circle/area of small circle

Area=π×R×R/π×r×r

Area=(R/r)^2(put value of R in given )

=4×4

=16