If the circumference of a circle is $\pi $ units more than the diameter of the circle then find the diameter of the circle.
VerifiedHint: In the above question we will have to know about the circumference of the circle. Circumference of the circle or the perimeter of the circle is the measurement of the boundary across any two-dimensional circular shape including the circle. The circumference or perimeter of a circle \[=2\pi R=\pi D\] where R is the radius of the circle, D is the diameter of the circle and \[\pi \] is the mathematical constant with an approximate value of 3.14.
Complete step-by-step answer:
Let us suppose the diameter of the circle is D units.
Now, in the above question, we have been given that the circumference of a circle is \[\pi \] units more than the diameter of the circle.
So, we will use the formula of the circumference of circle and we get as follows:
\[\pi D=D+\pi\]
\[\Rightarrow \pi D-D=\pi\]
\[\Rightarrow D\left( \pi -1 \right)=\pi\]
\[\Rightarrow D=\dfrac{\pi }{\left( \pi -1 \right)}\]
As we know that the value of $\pi $ is equal to 3.14(approximately).
So, by substituting the value of $\pi $ in the above expression we get,
\[D=\dfrac{3.14}{3.14-1}\]
\[\text{ = }\dfrac{3.14}{2.14}\]
\[\text{ = 1}\text{.46 units}\]
Therefore, we get the diameter of the circle is 1.46 units (approximately).
Note: Just remember the formula of the circumference of a circle as it will help you in these types of questions. Also, be careful while doing calculations. Also, remember the fact about $\pi $ that it is the ratio of circumference to the diameter of any circle.
