Question

Find the radius and diameter of a circular whose circumference is 440 cm.

Answer 1

Hint: Circumference is the total length of the boundary of any two-dimensional body. In the case of the circle, it is represented by \[\pi d\] where \[d\]is the diameter of the circle. The diameter of a circle is the straight line in the circle, which passes through the center of the circle, and both endpoints touch the circle. Diameter is also known as the longest chord of the circle where the chord is the straight lines whose endpoint touches the boundary of the circle, and these lines may or may not pass through the center. But, the radius of the circle is totally different as it is a line just from the center and end to the circle boundary. The radius and diameter of a circle are related \[r = \dfrac{d}{2}\].

Complete step by step answer:
Given the circumference of the circle
\[C = \pi d\], where \[d\]is the diameter which we are asked to find
So, \[d = \dfrac{C}{\pi }\]
The value\[\pi \]is either \[\dfrac{{22}}{7}\]or, \[3.14\], since nothing has been given in the question we will take\[\pi = \dfrac{{22}}{7}\]for our convenience, hence
\[
  d = \dfrac{{440}}{{\dfrac{{22}}{7}}} \\
   = 440 \times \dfrac{7}{{22}} \\
   = 140cm \\
 \]
Now we have to find the radius which is the half of the diameter denoted as \[r = \dfrac{d}{2}\]
So, the radius of the circular will be
\[r = \dfrac{d}{2} = \dfrac{{140}}{2} = 70cm\]
Hence the diameter and the radius of the circle whose circumference is \[400cm\]are\[140cm\]and\[70cm\] respectively.

Note: The value of \[\pi \]is given either as \[3.14\]or\[\dfrac{{22}}{7}\]is basically a constant term referred to as the ratio of the circumference of the circle to its diameter. If in the question, the value of \[\pi \]has been specified then, use that value only.