Question

the circumference of two circles r in the ratio 2:3 .find the ratio of their areas
​

Answer 1

Given: The circumference of two circles r in the ratio 2:3.

Need to find: The ratio of their areas.

❒ Let the radius of two circles be $\sf r_{1}$ and $\sf r_{2}$

⠀⠀⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━━━⠀

⠀⠀⠀

$\underline{\bf{\dag} \:\mathfrak{As\: we \; know \: that\; :}}$

⠀

$\star\:\boxed{\sf{\purple{ Circumference\; of\:circle = 2 \pi r}}}$

⠀⠀⠀

$:\implies\sf r_{1} : r_{2} = 2:3$

⠀⠀⠀

» To find the ratio of their areas,

⠀⠀⠀

$\star\:\boxed{\sf{\pink{\pi r^{2}_{1} : \pi r^{2}_{1}}}}$

⠀⠀⠀

$:\implies\sf Area_{\:(ratio)} = \bigg(\dfrac{r_{1}}{r_{2}}\bigg) \\\\\\:\implies\sf Area_{\:(ratio)} = \bigg(\dfrac{2}{3}\bigg)^2 \\\\\\:\implies\sf Area_{\:(ratio)} = \bigg(\dfrac{4}{9}\bigg) \\\\\\:\implies{\underline{\boxed{\frak{\purple{ Area_{\:(ratio)} = 4:9}}}}}\:\bigstar$

⠀⠀⠀

$\therefore\:{\underline{\sf{Hence, \ the\; ratio\: of \: their \: areas \: \ is\: \bf{4:9}.}}}$

Answer 2

Answer:

Given :-

The circumference of two circles r in the ratio 2:3.

To Find :-

Ratio of areas

Solution :-

Let the radius be r and r'

r:r' = 2:3

ratio of their areas,

Area of circle = πr²

r:r' = (2/3)²

r:r' = (4/9)

Therefore :-

$\sf \: Ratio = 4 \ratio9$