Question

A piece of wire $72$cm long is cut into two equal pieces and each is formed into a circle.

What is the sum, in square centimeters, of the areas of these circles $?$

Answer 1

Find the areas of two circles formed:

Length of a wire is $72$ cm.

Length of each piece of wire $=\frac{72}{2}=36$ cm.

Recall the formula of circumference of circle:

$C=2\mathrm{\pi r}$

Let $r$ be the radius of each piece of wire.

Since the circumference of the circle is equal to length of each piece of wire, we get:

$2\times \mathrm{\pi }\times \mathrm{r}$$=36$ ; $[\mathrm{\pi }=\frac{22}{7}]$

$\Rightarrow$ $r=\frac{36\times 7}{2\times 22}$

$\therefore$ $r=\frac{63}{11}$cm

Find the area of each circle. ; $[A={\mathrm{\pi r}}^2]$

$A=\frac{22}{7}\times {\left(\frac{63}{11}\right)}^2$

$\Rightarrow$ $A=\frac{1134}{11}$$=103.09\text{square}\mathrm{centimeters}$

The sum of areas of two circle will be as follows:

$$\begin{gathered} =103.09+103.09 \\ =206.18\text{square centimeters.} \end{gathered}$$

Hence, the sum of areas of these circle is $206.18\text{square centimeters.}$