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
[tex]C= \pi d[/tex]
Substituting the value of C, we will get
[tex]19.5= \pi d \\ d = \frac{19.5}{ \pi}[/tex]
When the diameter increased by 3, then the circumference is
[tex]C = \pi ( \frac{19.5}{ \pi} +3})=Approx 29 inches[/tex]
And the circumference , when diameter is increased by 3 is 29 inches .
Since the circumference of a circle = 19.5 inches
[tex]2\Pi r = 19.5[/tex]
[tex]2 \times \frac{22}{7} \times r = 19.5[/tex]
[tex]r = \frac{19.5 \times 7}{22 \times 2}[/tex]
r = 3.1 inches
So, diameter = 2r = [tex]2 \times 3.1 = 6.2[/tex] inches.
Since. the diameter of new circle is reduced by three.
Therefore, D = 6.2-3 = 3.2 inches.
R = 3.2 [tex]\div 2 = 1.6[/tex] inches
Now, circumference of new circle
= [tex]2 \pi r[/tex]
= [tex]2 \times \frac{22}{7} \times 1.6[/tex]
=10 inches
So, the circumference of the new circle is 10 inches.
