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

$2\Pi r = 19.5$

$2 \times \frac{22}{7} \times r = 19.5$

$r = \frac{19.5 \times 7}{22 \times 2}$

r = 3.1 inches

So, diameter = 2r = $2 \times 3.1 = 6.2$ inches.

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

Therefore, D = 6.2-3 = 3.2 inches.

R = 3.2 $\div 2 = 1.6$ inches

Now, circumference of new circle

= $2 \pi r$

= $2 \times \frac{22}{7} \times 1.6$

=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

$19.5= \pi d \\ d = \frac{19.5}{ \pi}$

When the diameter increased by 3, then the circumference is

$C = \pi ( \frac{19.5}{ \pi} +3})=Approx 29 inches$

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