Question

the ratio of the circumference of two circle s is 3:4. find the ratio of their areas.​

Answer 1

Step-by-step explanation:

Circumference of circle C1 = 2πr1

Circumference of circle C2 = 2πr2

C1/C2 =2πr1/2πr2

r1/r2=3/4

area of circle r1/area of circle r2=πr1^2/πr2^2=(r1/r2)^2=(3/4)^2

∴ Ratio of two circles = 9: 16

Answer 2

Answer:

$\large\boxed{\sf{9:16}}$

Step-by-step explanation:

Let the circumference of both the circles is c1 and c2 respectively.

Therefore, c1: c2 = 3:4

We know that, Circumference of a Circle having radius r is given by 2πr.

Let the radius of both the circles is r1 and r2 respectively.

Therefore, according to question,

$\sf{= > \dfrac{c1}{c2} = \dfrac{2\pi \: r1}{2\pi \: r2} }\\ \\ \sf{= > \dfrac{2\pi \: r1}{2\pi \: r2} = \dfrac{3}{4} } \\ \\ \sf{ = > \dfrac{r1}{r2} = \dfrac{3}{4} } \: \: \: \: \: \: \: \: \: \: \: \: \: \: ................(1)$

We know that, Area of a circle having radius ,r is given by $\pi {r}^{2}$.

Let the area of both circles is a1 and a2 respectively.

$\sf{= > \frac{a1}{a2} = \frac{\pi {r1}^{2} }{\pi {r2}^{2} } }\\ \\ \sf{ = > \frac{a1}{a2} = {( \frac{r1}{r2} )}^{2} } \\ \\ \sf{ = > \frac{a1}{a2} = {( \frac{3}{4} )}^{2}\:\:\:\:\:\:from\:(1) } \\ \\ \sf{ = > \frac{a1}{a2} = \frac{9}{16} }$

Hence, ratio of areas is 9:16