Question

A piece of wire in the from of a rectangle 8.6cm long and 5.7cm broad,is reshaped into the from of a circle. find the diameter of the circle. (take π 22/7)​

Answer 1

Answer :

• Diameter of the circle is 9.1 cm

Explanation :

Given :

• Length of the rectangle = 8.6 cm.

• Breadth of the rectangle = 5.7 cm.

• Value of π = 22/7

To find :

• Diameter of the circle , d = ?

Solution :

Perimeter of the rectangle :

We know the formula for perimeter of a Rectangle , i.e,

⠀⠀⠀⠀⠀⠀⠀⠀⠀P = 2(l + b)

Where,

• P = Perimeter
• l = length
• b = breadth

Now by using the formula for perimeter of a Rectangle and substituting the values in it, we get :

==> P = 2(l + b)

==> P = 2(8.6 + 5.7)

==> P = 2 × 14.3

==> P = 28.6

∴ P = 28.6 cm

Hence the perimeter of the rectangle is 28.6 cm.

According to the Question , the circle is made from the same wire (which was in the shape of the rectangle) , hence the perimeter of the circle will be equal to the perimeter of the rectangle.

∴ Perimeter of circle = Perimeter of the rectangle

We know the formula for perimeter of a circle i.e,

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀C = πd

Where,

• C = Circumference of the Circle
• d = Diameter

Now by using the formula for perimeter of a Circle and substituting the values in it, we get :

==> C = πd

==> 28.6 = 22/7 × d

==> 28.6 × 7/22 = d

==> 200.2/22 = d

==> 9.1 = d

∴ d = 9.1 cm

Therefore,

• The diameter of the circle is 9.1 cm.

Answer 2

$\huge{\boxed{\rm{\red{Question}}}}$

A piece of wire in the from of a rectangle 8.6cm long and 5.7cm broad,is reshaped into the from of a circle. find the diameter of the circle. (take π 22/7)

$\huge{\boxed{\rm{\red{Answer}}}}$

${\bigstar}\large{\boxed{\sf{\pink{Given \: that}}}}$

• Length of Rectangle = 8.6 cm
• Breadth of Rectangle = 5.7 cm
• Value of π ( pi ) = 22/7

${\bigstar}\large{\boxed{\sf{\pink{To \: find}}}}$

• Diameter of circle

${\bigstar}\large{\boxed{\sf{\pink{Solution}}}}$

We know that, the perimeter of Rectangle ☞

$\large\green{\texttt{2 ( length + breadth )}}$

We also write -

Perimeter as - p

Length as - l

Breadth as - b

☞ Now by using the formula of perimeter of Rectangle we substitute the values and we get the following results →

P = 2 × 14.3

P = 28.6 cm

$\large\green{\texttt{So, perimeter is 28.6 cm}}$

☞ According the question circle is made from the same wire { which was in the rectangular shape } , hence the perimeter

of the circle wil equal to the perimeter of Rectangle.

Therefore, Perimeter of circle = Perimeter of rectangle.

We know the formula of perimeter of circle,

$\large\green{\texttt{C = πd}}$

We also write -

Circumference as - c

Diameter as - d

☞ Now using the formula of perimeter of the circle and substituting the value we get,

• C = πd
• 28.6 = 22/7 × d
• 28.6 × 7/22 = d
• 200.2/22 = d
• 91.1 = d
• d = 91.1

Hence the diameter = 91.1

@Itzbeautyqueen23

Hope it's helpful

Thank you :)