Question

If the diameter of a circle with a circumference of 19.5 inches is reduced by three, what would be the circumference of the new circle?

Answer 1

Since the circumference of a circle = 19.5 inches

`2\Pi r = 19.5`

`2 * (22)/(7) * r = 19.5`

`r = (19.5 * 7)/(22 * 2)`

r = 3.1 inches

So, diameter = 2r =
`2 * 3.1 = 6.2` inches.

Since. the diameter of new circle is reduced by three.

Therefore, D = 6.2-3 = 3.2 inches.

R = 3.2
`/ 2 = 1.6` inches

Now, circumference of new circle

=
`2 \pi r`

=
`2 * (22)/(7) * 1.6`

=10 inches

So, the circumference of the new circle is 10 inches.

Answer 2

It is given that the circumference of the circle is 19.5 inches. Let the diameter is d inches .

And the formula of circumference is

`C= \pi d`

Substituting the value of C, we will get

`19.5= \pi d \\ d = (19.5)/( \pi)`

When the diameter increased by 3, then the circumference is

`C = \pi ( (19.5)/( \pi) +3})=Approx 29 inches`

And the circumference , when diameter is increased by 3 is 29 inches .