Question

A wire is in the form of a circle of radius 42 cm. It is bent into a square. The side
of the square is:
(a) 56 cm
(b) 66 cm
(c) 52 cm
(d) 72 cm​

Answer 1

Answer:

$\huge \bf \: given$

• Wire in the form of circle has radius = 42 cm

$\huge \bf \: to \: find$

Side of square

$\huge \bf \: required \: answer$

As we are knowing that the wire has a radius of 42 cm.

So, we will find circumference of circle

Circumference of circle = Length of wire

$\small { \bf \: {\underline {circumference \: of \: circle \: = 2 \pi\: {r}^{} }}}$

$\sf \: circumference \: = 2 \times \frac{22}{7} \times {42}$

$\sf \: circumference \: = 2 \times \frac{22}{7} \times 42$

$\sf \: circumference \: = 2 \times 22 \times 6$

$\sf \: circumference \: = 264 \: cm$

Now,

As we know that

$\huge \bf \: side \: = \frac{perimeter}{4}$

$\sf \: side \: = \frac{264}{4}$

$\sf \: side \: = 66 \: cm$

$\sf \: hence \: side \: of \: square \: to \: bent \: = 66 \: cm$

Answer 2

GIVEN :-

• Radius of Circle ( r ) = 42 cm.

TO FIND :-

• The side of square.

SOLUTION :-

As we know that,

⇒ Perimeter of Circle = 2πr

⇒ Perimeter of Circle = 2 × 22/7 × 42

⇒ Perimeter of Circle = 44/7 × 42

⇒ Perimeter of Circle = (44 × 42)/7

⇒ Perimeter of Circle =1848/7

⇒ Perimeter of Circle = 264 cm.

Now , If the wire is bent into a square , So the Perimeter of circle is equal to the Perimeter of a square i.e,

⇒ Perimeter of square = Perimeter of Circle

⇒ Perimeter of square = 264 cm.

⇒ 4 × side = 264 cm.

⇒ side = 264/4 cm

⇒ side = 66 cm.

Hence the side of the square is 66 cm.