Question

The area of a square is $100c{m}^2$. The circumference (in $cm$) of the largest circle cut of it is

• A. $5\mathrm{\pi }$
• B. $10\mathrm{\pi }$
• C. $15\mathrm{\pi }$
• D. $20\mathrm{\pi }$

Answer 1

The correct option is B

$10\mathrm{\pi }$

Explanation for the correct options:

Step 1: Find the side of the square:

Let us assume the side of the square be $S$

From the given details we note that

Area of a square is $100c{m}^2$

We know that,

Area of square $={\left(side\right)}^2$

So,

$$\begin{gathered} S^2=100c{m}^2 \\ \Rightarrow S=\sqrt{100} \\ \Rightarrow S=10cm \end{gathered}$$

Thus the side of the square is $10cm$

Step 2: Find the radius of the circle:

Now, for the largest circle in the square, a diameter of the circle must be equal to the side of the square.

Diameter $=$ side of square$=10cm$

Let $r$be the radius then the diameter is $2r$

So,

$$\begin{gathered} 2r=10cm \\ \Rightarrow r=\frac{10}{2} \\ \Rightarrow r=5cm \end{gathered}$$

Step 3: Find the circumference of the circle

Now,

$\begin{array}{rcl}\mathbf{circumference}\mathbf{}\mathbf{of}\mathbf{}\mathbf{circle}\mathbf{}& \mathbf{=}& \mathbf{}\mathbf{2}\mathbf{\pi r}\mathbf{}\mathbf{}\\ & =& 2\times \pi \times 5\\ & =& 10\pi \end{array}$

Thus, the circumference of the circle is $10\mathrm{\pi }$

Hence, the correct option is (B)