Question

Liam wants to cut the largest piece of square possible out of a circular piece of cloth. If the area of the cloth is 128π sq inches, find the side length of the square.

• A. 12 inches
• B. 8 inches
• C. 16 inches
• D. 4 inches

Answer 1

The correct option is C 16 inches

The largest square that can be inscribed in a circle has a diagonal equal to the diameter of the circle.

Let the side length of the square be "x".

Then, by forming the largest square that fits the circle, we get:


Using the Pythagoras theorem, we get:

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

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

$Area=\pi \times (Radius{)}^2=128\pi \text{sq. inches}$

$⟹(Radius{)}^2=128$
$⟹\frac{x^2}{2}=128$

$⟹x^2=256$
$⟹x=\sqrt{256}=16\text{inches}$

Hence, the side length of the largest possible square that can be cut out of the circle is 16 inches.