Question

Difference between the circumference and the diameter of the circle is 60 cm then what is the radius of the circle
with full explanation​

Answer 1

Given :

Difference between the circumference and the diameter of the circle is 60 cm.

To find :

Radius of the circle .

Solution :

Let radius of circle be "r" cm

∴ Diameter of circle = 2r cm

∴ Circumference of circle = 2πr cm

Now atq,

⇒ 2πr - 2r = 60

⇒ 2r(π - 1) = 60

⇒ 2r = 60/(π - 1)

⇒ 2r = 60/(22/7 - 1 )

⇒ 2r = 60/(15/7)

⇒ 2r = 60 × (7/15)

⇒ 2r = 28

⇒ r = 28/2

⇒ r = 14 cm

∴ Radius of circle = 14 cm.

Answer 2

★ Given:

The difference between the circumference and the diameter of a circle is 60 cm.

★ To Find:

The radius of the circle.

★ Solution:

Diameter of a circle = 2r

Circumference of a circle = 2πr

It is given that the difference between the circumference and diameter of the circle is 60 cm.

Forming an equation:

$\sf{2\pi\:r-2r=60}$

→ Taking out the common values in each term.

$\sf{2r(\pi-1)=60}$

→ Substituting the value of π as 22/7.

$\sf{2r(\dfrac{22}{7}-1)=60}$

→ Equivalizing the denominators in the fraction.

$\sf{2r(\dfrac{22-7}{7})=60}$

→ Appling the operations on the fraction.

$\sf{2r\times\dfrac{15}{7}=60}$

→ Moving the constants to the RHS.

$\sf{r=60\times\dfrac{7}{15}\times\dfrac{1}{2}}$

→ After dividing the common factors.

$\sf{r=7\times2}$

$\sf{r=14\:cm}$

Hence the radius of the circle is 14 cm.

★ Verification:

We can apply the value of the radius to find the circumference and diameter. When we subtract, and get the required number as given in the question, our answer is verified.

Diameter = 2r = 2 x 14 = 28 cm

Circumference = 2πr = 2 x 22/7 x 14 = 88 cm

It is given that:

2πr - 2r = 60

88 - 28 = 60

LHS = RHS

Hence Verified!