Question

The radius of a circle is $5.5$ centimetres. What is the circumference in metres?

Answer 1

Hint: Here in this question we want to find the circumference of a circle and whose radius is $5.5$ centimetres. We have a standard formula for finding the circumference of a circle when we are provided with the radius of the circle, $C = 2\pi r$. We know the value of $\pi $ and the value of radius is given to us in the question itself. We substitute known values and determine the circumference of a circle using the formula.

Complete step by step answer:
The circle is a two dimensional figure and we have to determine the circumference when radius is given to us as $5.5$ centimetres. The unit for the circumference is square units. In the given question, we are given the length of the radius in centimetres. So, we will get the circumference of the circle using the formula in the unit $cm$.

To find the area of a circle, we use formula $C = 2\pi r$. Substituting the value of radius, we get,
$ \Rightarrow C = 2\pi \left( {5.5} \right)$ centimetres
Carrying out the multiplication,
$ \Rightarrow C = 11\pi $ centimetres
Putting the value of $\pi $, we get,
$ \Rightarrow C = 11 \times \dfrac{{22}}{7}$ centimetres
Cancelling the common factors in numerator and denominator, we get,
$ \Rightarrow C = \dfrac{{242}}{7}$ centimetres
$ \Rightarrow C = 34.57$ centimetres
Therefore, the circumference of a circle with a radius $5.5$ centimetres is $34.57$ centimetres.

Now, we have to convert this circumference into metres. So, we know that one metre consists of a hundred centimetres.
Hence, $1\,m = 100\,cm$.
Dividing both sides by hundred, we get,
$ \Rightarrow 1\,cm = \dfrac{1}{{100}}\,m$
Multiplying both sides by $34.57$ to find the conversion of $34.57$ centimetres to metres.
$ \Rightarrow 34.57\,cm = \dfrac{{34.57}}{{100}}\,m$
Now, we know that the division by powers of ten is easy as we just have to shift the decimal point to the left of the same number of digits as the number of zeroes in the power of ten. So, there are two zeros in a hundred. Hence, we shift the decimal point to two places towards the left. Hence, we get,
$ \Rightarrow 34.57\,cm = 0.3457\,m$

Therefore, the circumference of a circle with a radius $5.5$ centimetres in metres is $0.3457$.

Note: A circle is a closed two dimensional figure. Circumference of a circle is the length of the arc of the circular field. To determine the circumference of a circle we have the standard formula $C = 2\pi r$ where r represents the radius. The radius of a circle is the line segment which joins the centre of the circle to any point on the circle or to the circumference. The radius is denoted as ‘R’ or ‘r’.