Question

The diffierence bettween circulumfernce and radius of the circle is 37 cm what is the circulumfernce of the circle

Answer 1

Appropriate Question :

The difference between circumference and radius of the circle is 37 cm. What is the circumference of the circle?

Required Solution :

Given:-

• The difference between circumference and radius of the circle is 37 cm.

To find:-

• Circumference of the circle

Calculation:-

In order to find the circumference of the circle, firstly we have to find the radius(r) of the circle.

★ $\boxed{\sf{ Circumference \: of \: \: circle = 2\pi r}}$

According to the question:

$\longrightarrow$ Circumference – radius = 37cm

$\sf { \longrightarrow (2 \pi r) - r =37}$

[Value of π is 22/7 ]

$\sf { \longrightarrow \Bigg(2 \times \dfrac{22}{7} \times r \Bigg )- r =37}$

$\sf { \longrightarrow \Bigg ( \dfrac{44}{7}r \Bigg ) - r =37}$

$\sf { \longrightarrow \dfrac{44r - 7r}{7} =37}$

$\sf { \longrightarrow \dfrac{37r}{7} =37}$

$\sf { \longrightarrow 37r = 37 \times 7 }$

$\sf { \longrightarrow 37r = 259 }$

$\sf { \longrightarrow r = \dfrac{259}{37} }$

$\sf \red { \longrightarrow r = 7 \: cm}$

Now,

★ $\boxed{\sf{ Circumference \: of \: circle = 2\pi r}}$

Substituting values :

$\sf { \longrightarrow C = 2 \times \dfrac{22}{7} \times 7 }$

[ 7 cancelled out from both denominator and numerator. ]

$\sf { \longrightarrow C = 2 \times 22 }$

$\sf \red { \longrightarrow C = 44 \: cm }$

Therefore, circumference of the circumference is 44 cm.

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More points about circles :

• Circumference is also called perimeter of the circle.

• Diameter of the circle = 2R

• Area of circle = πr²

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Answer 2

We have,

Difference between circumference and radius = 37 cm

We know, circumference = 2πr

According to the Question,

2πr - r = 37

⇒ r(2π - 1) = 37

⇒ r(44/7 - 1) = 37

[∵ π = 22/7 (taken) and 2 × 22/7 = 44/7]

⇒ r[⅐(44 - 7)] = 37

⇒ r[37/7] = 37

⇒ r = 37 × 7/37

⇒ r = 7 cm

Now, circumference = 2πr = 2 × 22/7 × 7 = 44 cm.