Question

the ratio between the radii of two circle is 5 :7 the ratio between their (i)circumference (ii)areas

Answer 1

So lets consider the radius of two circles be:-
5r and 7r

i ) Circumference of Circle one =
$2\pi \times r$
$2\pi \times 5r$

=> Circumference of Circle two =
$2\pi \times 7r$

$ratio = \frac{circumference \: of \: circle \: one}{circumference \: of \: circle \: two} \\ = \frac{2\pi \times 5r}{2\pi \times 7r} \\ = \frac{5}{7} \\ = 5:7$

ii ) Area of Circle one =
$\pi \times {r}^{2}$
$= \pi \times {(5r)}^{2} \\ = \pi \: \times \: 25 {r}^{2}$
=> Area of Circle two =
$= \pi \: \times {(7r)}^{2} \\ = \pi \: \times {49r}^{2}$

$ratio = \frac{area \: of \: circle \: one}{area \: of \: circle \: two} \\ = \frac{\pi \times 25 {r}^{2} }{\pi \times 49 {r}^{2} } \\ = \frac{25}{49} \\ = 25:49$

Solutions
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i ) 5:7

ii ) 25:49



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