Question

Find the diameter of the circle whose circumference is $1256cm$. Use $\pi = 3.14$.

Answer 1

Hint: We will divide diameter by $2$ to get the radius. Further we will substitute the value of radius in the formula of circumference of the circle to the answer.
By using the formula of circumference of circle $ = 2\pi r\,\,or\,\pi d$
Here $r - radius$
$d - diameter$


Complete step by step solution:
As, we know that circumference of circle $ = 2\pi r$
And $r - radius$
So, according to question
Circumference $ = 1256$
And $\pi = 3.14$
Then, using formula of circumference, we will get
Circumference of circle $ = 2\pi r$
$1256 = 2\pi r$
$\dfrac{{1256}}{2} = \pi r$
$\dfrac{{628}}{\pi } = r$ $....(i)$
Now, we calculate the value of $r$, we will get
$ \Rightarrow r = \dfrac{{628}}{{3.14}}$
$r = \dfrac{{628 \times 100}}{{314}}$
$r = \dfrac{{314 \times 100}}{{157}}$
$r = \dfrac{{2 \times 100}}{1}$
$r = 200$
Therefore, the radius is $200cm$ and $d = 2r$
Now, we will substitute the value of $r$, we have
$
  d = 2 \times 200 \\
  d = 400cm \\
 $
Thus, the diameter of circle is $400cm$


Additional Information: Circumference or perimeter of the circle, is the measurement of the boundary of the circle.


Note: Students should use the value of $\pi $ if it is mentioned in the question otherwise you can take $\dfrac{{22}}{7}$or $3.14$. We know that \[d = 2r\]so we use the direct formula of circumference of circle $ = \pi d$to the answer.