Question

The ratio between the radius of two circles is 5 : 7. Find the ratio between their:
(i) circumference
(ii) areas

Answer 1

(i) The ratio of the radius of the circles = 5 : 7
Let radius of first circle = 5x
and radius of second circle = 7x

∴ Circumference of first circle = 2πr

= 2π × 5x = 10πx

and circumference of second circle

= 2π × 7x = 14πx

∴ Ratio between their circumference

= 10πx : 14πx

= 10 : 14 = 5 : 7

(ii) Area of first circle = πr²

= `22/7xx5"x"xx5"x"=550/7"x"^2`

and area of second circle = πr²

= `22/7xx7"x"xx7"x"=1078/7"x"^2`

Ratio between their areas

= `550/7"x"^2:1078/7"x"^2`

= 550 : 1078 ............(Dividing by 22)

= 25 : 49