Question

Find the circumference and area of the circle of radius 4.2 cm.

Answer 1

Hint: Here, we can calculate the circumference of the circle using the formula $Circumference=2\times \pi \times r$ and we can calculate the area if the circle using the formula $Area=\pi \times {{r}^{2}}$.

Complete step-by-step answer:

In geometry the circumference of a circle is the perimeter of a circle. That is, the circumference will be the arc length of the circle, as if it were opened up and straightened out to a line segment. More, generally, the perimeter is the curve length around any closed figure.
The circumference of a circle may be defined as the limit of the perimeters of inscribed regular polygons as the number of sides increases without bound or Circumference of a circle is the length of the boundary of the circle. The term circumference is used when measuring physical objects as well as when considering abstract geometric forms.
The area enclosed by a circle of radius r is given by the formula $A=\pi {{r}^{2}}$. Here, $\pi $ represents a constant, approximately equal to the ratio of the circumference of any circle to its diameter.
Here, we have been given that the radius of the circle is = 4.2 cm.
Therefore circumference of the circle will be:
$\begin{align}
  & C=2\times \pi \times r \\
 & \Rightarrow C=2\times \dfrac{22}{7}\times 4.2cm=26.4cm \\
\end{align}$
Also, the area of the circle will be :
$\begin{align}
  & A=\pi {{r}^{2}} \\
 & \Rightarrow A=\dfrac{22}{7}\times 4.2\times 4.2c{{m}^{2}}=55.44c{{m}^{2}} \\
\end{align}$
Hence, the circumference and the area of the circle is 26.4 cm and 55.44 $c{{m}^{2}}$ respectively.

Note: Students should remember the definitions and formulas for calculating the circumference and area of a circle. If radius of circle is given in terms of diameter then we should convert into radius by using relation ${Radius=\dfrac{Diameter}{2}}$ then we can calculate circumference of circle or we can use direct formula $C=\pi \times d$. The calculations part must be done carefully to avoid unnecessary mistakes.