Question

A rectangular loop of length 50 cm and width 38 cm is converted into a circular loop. find the radius of the circular loop​

Answer 1

Given:

• Length ( Rectangle) = 50cm
• Breadth (Rectangle) = 38 cm

To Find:

• Radius of Circular Loop?

Formula Used:

$\\ \bigstar{\underline{\boxed{\tt\large\green{ Perimeter_{(Rectangle)} = 2(l + b) }}}}$

Where

• l = Length
• b = Breadth

Solution:

After substituting values,

$\implies$ P = 2(l + b)

$\implies$ P = 2(50 + 38)

$\implies$ P = 2( 88 )

$\implies$ P = 2 × 88

$\implies$ P = 176 cm

Hence,

• The Perimeter of the Rectangular loop is 176 cm.

________________________

$\\ \bigstar{\underline{\boxed{\tt\large{ \pink{ Perimeter \ Or \ Circumference_{(Circle)} } = 2πr }}}}$

:: Rectangular loop is converted into Circular Loop so, Perimeter of Rectangle is Equal to that of Circular shape.

• Perimeter of Rectangle = Perimeter of Circle
• 176 cm = 176 cm

$\implies$ P = 2πr

$\implies$ 176 = 2 × 22/7 × r

$\implies$ 176 × 7/22 × 2 = r

$\implies$ 28 cm = r

Hence,

• The Radius of the Circular Loop is 28cm.

$\bigstar{\underline{\tt\pink{ Formula \ related \ to \ Topic :- }}}$

$\\ \bullet \: \: {\sf\red{ Perimeter_{(Rectangle)} = 2(l + b) }} \\ \\ \bullet \: \: {\sf\large\red{ Circumference_{(Circle)} = 2πr }} \\ \\ \bullet \: \: {\sf\large\purple{ Area_{(Circle)} = πr^2 }}$

Answer 2

Question :

A rectangular loop of length 50 cm and width 38 cm is converted into a circular loop. find the radius of the circular loop.

Answer :

$\sf\red{Given:}$

• Length of the rectangular loop formed is 50 cm.

• Breadth of the rectangular loop formed is 38 cm.

• the loop is then converted to a circular loop .

$\sf\red{To\:Find:}$

• What is the radius of the circular loop so formed = ?

Explanation :

Perimeter of the rectangular loop = circumference of the circular loop .

Reason :

because the rectangular loop was transformed to circular loop .

$\sf\purple{Perimeter \:of \:the\: rectangular \:loop = 2×(l+b)}$

• l means length

• b means breadth or width .

$\longrightarrow\sf{2×(50+38)}$

$\longrightarrow\sf{2× 88}$

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

• Circumference of the circular loop = 176 cm

$\sf\purple{Circumference \:of \:the\: circular\: loop = 2πr}$

$\longrightarrow\sf{176 = 2×22/7 × r}$

$\longrightarrow\sf{176 = 44r/7 }$

$\longrightarrow\sf{176 × 7 = 44r }$

$\longrightarrow\sf{1232 = 44r }$

$\longrightarrow\sf{1232/44 = r }$

$\longrightarrow\sf\pink{ r = 28 cm}$

• Therefore the radius of the circular loop is 28 cm

@MissOxford