Question

A wire is looped in the form of a circle of radius 28 cm. it is bent again into a square form. what will be the length of the diagonal of the largest square possible thus?

Answer 1

First Find the area of the circle
Ar (circle)=22/7×28×28
=22×4×28
=88×28
=2464cm2
now, area of square=a×a (a: side of square)
a×a=2464
a2=2464
a=root of 2464
a=49.63 (aprox.)
now diagonal of square=aSquare+aSquare=(length of diagonal)square -Pythagoras theorem.
we know aSquare=2464
therefore aSqr+aSqr = 2464+2464
=4928cmSqr.
now Diagonal D= root of 4928
=70.19cm (approx.)

Answer 2

Length of the wire = Circumference of the circle

$\longrightarrow$ $\sf{(2 \times \frac{22}{7} \times 28)cm}$

$\longrightarrow$$\sf{176cm}$

Perimeter of the square = Length of the wire = 176cm

Hence, the side of the square = $\sf{\frac{176}{4}cm}$

$\longrightarrow$${\boxed{\sf{44cm}}}$