Question

The circumference of a circle is 106.76 centimeters. What is the circle's diameter?

Answer 1

Answer:

Given :-

• The circumference of a circle is 106.76 cm.

To Find :-

• What is the diameter of a circle.

Formula Used :-

$\clubsuit$ Circumference of Circle Formula :

$\longmapsto \sf\boxed{\bold{\pink{Circumference_{(Circle)} =\: 2{\pi}r}}}$

$\clubsuit$ Diameter Formula :

$\longmapsto \sf\boxed{\bold{\pink{Diameter =\: 2r}}}$

where,

• r = Radius

Solution :-

First, we have to find the radius :

Given :

$\bigstar$ Circumference of Circle = 106.76 cm

According to the question by using the formula we get,

$\implies \sf 2 \times \dfrac{22}{7} \times r =\: 106.76$

$\implies \sf \dfrac{44}{7} \times r =\: \dfrac{10676}{100}$

$\implies \sf r =\: \dfrac{10676 \times 7}{100 \times 44}$

$\implies \sf r =\: \dfrac{74732}{4400}$

$\implies \sf\bold{\purple{r =\: 16.98\: cm}}$

Hence, the radius of a circle is 16.98 cm.

Now, we have to find the diameter of a circle :

Given :

$\bigstar$ Radius = 16.98 cm

According to the question by using the formula we get,

$\longrightarrow \sf Diameter =\: 2 \times 16.98$

$\longrightarrow \sf Diameter =\: 2 \times \dfrac{1698}{100}$

$\longrightarrow \sf Diameter =\: \dfrac{3396}{100}$

$\longrightarrow \sf\bold{\red{Diameter =\: 33.96\: cm}}$

$\therefore$ The diameter of a circle is 33.96 cm .