Question

What is the diameter of the circle that has a circumference of 15cm?

Answer 1

Hint: Use the circle properties, radius and diameter relation and just directly substitute the values of whichever term provided in the question and find the other one. All we need to do is find the diameter.

Complete step by step solution:
In the given question we need to find the diameter of the circle which is twice the radius of the same circle. Also, we know that the circumference of the circle is the length of the circle or with respect to other shapes we can say that circumference is the diameter of the circle.
Therefore, we get the figure same as shown below.

The circumference of the circle is given by the formula $C=2\pi r$ where r is the radius and 2r is twice the radius which is equal to diameter so the same formula can also be written as $C=\pi D$ where D is the diameter of the circle and C is the diameter of the circle.
Now, circumference is already given in the question and we want to find the diameter so we will invert the formula as $D={\displaystyle \frac{C}{\pi }}$ .
C=15cm
D=?
$\pi =3.14or{\displaystyle \frac{22}{7}}$
Now, substituting the values in the formula we get
$\begin{array}{rl}& D={\displaystyle \frac{15}{\pi }}\\ & \Rightarrow {\displaystyle \frac{15}{22}}\times 7\end{array}$
$C={\displaystyle \frac{105}{22}}$
Now multiplying 15 and 7 we get 105 and then dividing by 22 we 4.77.

Therefore, diameter of the circle is 4.77 cm when the circumference is 15cm.

Note: Now, we can also verify our answer by calculating the circumference of the circle by using the diameter which we obtain as our answer to the given question and hence correct it if there is some error. Also we can use any value of $\pi$ while calculating diameter or circumference.