Question

$\text{A tailor wants to cut the largest piece of square}\text{possible out of a circular piece of cloth. If the}\text{area of the cloth is}32\pi \text{sq. inches, then find the}\text{length of the side}\text{of the square.}$

• A. 4 inches
• B. 2 inches
• C. 6 inches
• D. 8 inches

Answer 1

The correct option is D 8 inches

$\text{Let the side of the square be}x.$

$\text{Then, forming the largest square that fits}\text{the circle, we get:}$


$\text{Using the Pythagoras theorem, we get:}$

$x^2+x^2=(2\times Radius{)}^2$
$⟹2x^2=4\times (Radius{)}^2$
$⟹\frac{x^2}{2}=(Radius{)}^2$

$\text{Now, the area of the circle is given as:}$

$Area=\pi \times (Radius{)}^2=32\pi \text{sq. inches}$
$⟹(Radius{)}^2=32$
$⟹\frac{x^2}{2}=32$
$⟹x^2=64$
$⟹x=\sqrt{64}=8\text{inches}$

$\text{Hence, the length of the side of the largest}\text{possible square that can be cut out of the}\text{circle will be 8 inches.}$