Question

If the diameter of a circle changes from 18 cm to 6 cm, how will the circumference change?

Answer 1

the answer would be multiplies by 1/3

Answer 2

The circumference of a circle is changes by
`(1)/(3)` .

Explanation:

Formula

`Circumference\ of\ a\ circle = 2\pi r`

Where r is the radius of the circle .

As given

If the diameter of a circle changes from 18 cm to 6 cm .

Initial diameter = 18 cm

`Initial\ radius = (Initial\ diameter)/(2)`

`Initial\ radius = (18)/(2)`

= 9 cm

`\pi = 3.14`

`Circumference\ of\ initial\ circle = 2* 3.14* 9`

= 56.52 cm

Final diameter = 6 cm

`Final\ radius = (Initial\ diameter)/(2)`

`Final\ radius = (6)/(2)`

= 3 cm

`\pi = 3.14`

`Circumference\ of\ final\ circle = 2* 3.14* 3`

= 18.84 cm

Thus

`(Circumference\ of\ final\ circle)/(Circumference\ of\ initial\ circle) = (18.84)/(56.52)`

`(Circumference\ of\ final\ circle)/(Circumference\ of\ initial\ circle) = (1)/(3)`

Therefore the circumference of a circle is changes by
`(1)/(3)` .