Question

the ratio of radii of two circles is 5:3. Find the ratiobof their circumference. Gamers Are Beast Yt channel​

Answer 1

Given :-

Ratio of two circle's radii = 5:3

To find :-

Ratio of their Circumference

What is ratio?

Ratio is the comparison of two quantities expressed in it's simplest form.

Therefore, the radii must be expressed in it's simplest form :- 5:3

Hence the actual radii must be a multiple of a certain number.

let that common number be x.

Ratio of the radii not in it's simplest form :- 5x:3x

The radii are 5x and 3x respectively.

Circumference of a circle = 2πr

Thus the ratio of the Circumferences will be :-

$\dfrac{2\pi \times 5x}{2\pi \times 3x}$

Cancelling the common factors :-

$\dfrac{ \cancel{2\pi} \times 5 \cancel{ x}}{ \cancel{2\pi} \times 3 \cancel{x}}$

The ratio of the two circle's circumferences will be :-

5 : 3

How to find the ratio of their areas :-

We know that,

Area of a circle = πr²

Thus the ratio of the areas will be :-

$\dfrac{\pi \times {(5x)}^{2} }{\pi \times {(3x)}^{2} }$

Cancelling the common terms :-

$\dfrac{ \cancel{\pi} \times 25 \cancel{ {x}^{2} }}{ \cancel{\pi} \times9 \cancel{ {x}^{2}} }$

The ratio of their areas will be :-

25:9

Some more formulas :-

Perimeter of a square = 4 × side

Area of a square = (side)²

Perimeter of a rectangle = 2(length+breadth)

Area of a rectangle = length × breadth

Perimeter of a parallelogram = 2(base+height)

Area of a parallelogram = base × height

Perimeter of a rhombus = 4 × side

Area of a rhombus =  ½ × Diagonal 1 × Diagonal 2