The difference between the circumference and radius of a circle is 30π . Find the diameter of the circle. - Sri Chaitanya Infinity Learn Best Online Courses for NCERT Solutions, CBSE, ICSE, JEE, NEET, Olympiad and Class 6 to 12

We have a circle of radius

r

.
Since we already know that the circumference of a circle is equal to

2 π r

,
By deducting the radius from the circumference and equating the result to the supplied variables, we create an equation.

⇒ 2 π r − r = 30 π

In the Left-Hand Side of the equation, take

r

common.

⇒ r (2 π − 1) = 30 π

Divide both sides of the equation by

(2 π − 1)

⇒ r (2 π − 1) (2 π − 1) = 30 π (2 π − 1)

Remove the identical terms from the denominator and numerator on both sides of the equation.

⇒ r = 30 π (2 π − 1)

Now we know that the length of diameter of the circle is twice the length of the radius of the circle.
Diameter of the circle with radius

r = 2 × 30 π (2 π − 1)

Diameter of the circle with radius

r = 60 π (2 π − 1)

∴

Diameter of the circle with radius '

r

' is

60 π (2 π − 1)

Hence, correct option is ‘2’

The difference between the circumference and radius of a circle is $30 π$ . Find the diameter of the circle.