Question

What is the circumference of a circle with a diameter of 50 mm?

Answer 1

Hint: Here in this question, we have to find the circumference of a circle. To determine the circumference of a circle we use the formula \[C = 2\pi r\], where r is the radius of the circle. Here we know the value of diameter using this we are going to determine the radius and then we are going to determine the circumference of a circle.

Complete step-by-step solutions:
Circumference of the circle or perimeter of the circle is the measurement of the boundary of the circle. Whereas the area of the circle defines the region occupied by it. If we open a circle and make a straight line out of it, then its length is the circumference. It is usually measured in units, such as cm or unit m.
When we use the formula to calculate the circumference of the circle, then the radius of the circle is taken into account. Hence, we need to know the value of the radius or the diameter to evaluate the perimeter of the circle.

Consider the given data, the diameter of a circle is 50 mm, where it represents in the millimeter.
As we know that the twice of the radius will be the diameter. Therefore, the radius will be half of the diameter.
Given, \[d = 50\,mm\]
Therefore, the radius will be \[r = \dfrac{d}{2} = \dfrac{{50}}{2} = 25\]
The radius of the circle is \[r = 25\,mm\].
Now the circumference of a circle is given by \[C = 2\pi r\]
On substituting the value of r in the formula we have
\[ \Rightarrow C = 2\pi \left( {25} \right)\]
On simplifying we have
\[ \Rightarrow C = 50\pi \]
\[\pi \] is a mathematical constant whose value is \[\pi = \dfrac{{22}}{7} = 3.14\], then
\[ \Rightarrow C = 50\left( {3.14} \right)\]
\[ \Rightarrow C = 157\,mm\]

Therefore, the circumference of a circle is \[157\,mm\].

Note: Here the circumference of a circle formula can be written as \[C = d\pi \], where d is the diameter and we also know that the radius is the half of the diameter and diameter is the twice of the radius. and we directly substitute the value of d and we get the solution. here we must mention the unit.