The largest possible square is inscribed in a circle having circumference $2 π$ units. The area of the square in the square units is
$4 π \sqrt{2}$ sq. units
$\sqrt{2}$ sq. units
$2 π \sqrt{2}$ sq. units
$2$ sq. units

Question

The largest possible square is inscribed in a circle having circumference $2 π$ units. The area of the square in the square units is
$4 π \sqrt{2}$ sq. units
$\sqrt{2}$ sq. units
$2 π \sqrt{2}$ sq. units
$2$ sq. units

Toppr Admin · Accepted Answer

Circumference - 2-x3C0-r-2-x3C0- -Given-x21D2- r-1 unit-x2234- Diagonal of square -2 unitsLet each side of the square -xA0-a units- Then-xA0-a2-a2-4-x21D2-2a2-4-x21D2-a-x221A-2-x21D2- Area of square - -x221A-2-x221A-2-2 sq units

The largest possible square is inscribed in a circle having circumference 2π units. The area of the square in the square units is4π√2 sq. units√2 sq. units2π√2 sq. units2 sq. units

Circumference = 2πr=2π (Given)⇒ r=1 unit∴ Diagonal of square =2 unitsLet each side of the square =a units. Then a2+a2=4⇒2a2=4⇒a=√2⇒ Area of square = (√2)(√2)=2 sq units

The largest possible square is inscribed in a circle having circumference $2 π$ units. The area of the square in the square units is
$4 π \sqrt{2}$ sq. units
$\sqrt{2}$ sq. units
$2 π \sqrt{2}$ sq. units
$2$ sq. units

Circumference $=$ $2 π r = 2 π$ (Given)
$\Rightarrow$ $r = 1$ unit
$∴$ Diagonal of square $= 2$ units
Let each side of the square $= a$ units. Then
$a^{2} + a^{2} = 4 \Rightarrow 2 a^{2} = 4 \Rightarrow a = \sqrt{2}$
$\Rightarrow$ Area of square $=$ $(\sqrt{2}) (\sqrt{2}) = 2$ sq units