Question

Find the diameter and radius of a circle with circumference = 6.28 cm.

Answer 1

Hint: Radius of a circle is the half the length of the diameter of a circle.
Diameter is the full width of the circle whereas the radius is the measure of the length from the center of the circle to any point on the circumference of the circle.
In this question the circumference of the circle is given so first we will substitute the given value in the circumference formula and then we will find the radius and then the diameter of the circle.
The circumference of the circle is given by the formula \[C = 2\pi r\].

Complete step by step answer:
Given the circumference of the circle \[C = 6.28cm\]
Now we know the circumference of a circle which is also known as the perimeter of the circle is given by the formula \[C = 2\pi r\], where \[r\] is the radius of the circle, now we will substitute the value of the circumference of the circle to find the radius taking \[\pi = 3.14\], hence we can write
\[
  C = 2\pi r \\
   \Rightarrow 6.28 = 2 \times 3.14 \times r \\
   \Rightarrow r = \dfrac{{6.28}}{{2 \times 3.14}} \\
   \Rightarrow r = \dfrac{2}{2} \\
   \Rightarrow r = 1cm \\
 \]
So the radius of the circle we get is \[r = 1cm\]
Now we know the radius of a circle is the half the length of the diameter of the circle, hence we can write
\[r = \dfrac{d}{2}\]
Since we already know the value of the radius of the circle, hence we can write the diameter of the circle is
\[
  d = 2r \\
   = 2 \times 1 \\
   = 2cm \\
 \]
Hence the diameter of the circle \[d = 2cm\].

Note: In a circle when a line a drawn from the center to any point on the circle then that line is known as the radius of the circle and when a line is dawn from a end point to the other end point passing through the center of the circle is known as diameter of a circle.