Question

What is the circumference and area of a circle with a diameter of 13 centimeters?

Answer 1

Hint: To solve this question we will use the formula of circumference of a circle and formula of area of a circle.
$\begin{align}
  & \text{Circumference}=2\pi r \\
 & \text{Area} =\pi {{r}^{2}} \\
\end{align}$
Here, r is the radius of a circle. By substituting the values in the above formula and simplifying the obtained equations we will get the desired answer.

Complete step-by-step solution:
We have been given a diameter of a circle that is 13 cm.
We have to find the circumference and area of a circle.
Now, we know that circumference of a circle is the perimeter of the circle which is given by the formula
 $\Rightarrow \text{Circumference}=2\pi r$
Here r is the radius of a circle.

Now, we know that $\text{Radius}=\dfrac{\text{diameter}}{2}$ , substituting the value we will get
$\begin{align}
  & \Rightarrow r=\dfrac{13}{2} \\
 & \Rightarrow r=6.5 \\
\end{align}$
Now, we know that $\pi =\dfrac{22}{7}or3.14$
Now, the circumference of a circle will be
$\Rightarrow \text{Circumference}=2\times 3.14\times 6.5$
Simplifying the above obtained equation we will get
$\Rightarrow \text{Circumference}=40.82cm$
Now, the area of a circle is given by the formula
$\Rightarrow \text{Area}=\pi {{r}^{2}}$
Now, substituting the values we will get
$\Rightarrow \text{Area}=3.14{{\left( 6.5 \right)}^{2}}$
Simplifying the above obtained equation we will get
$\begin{align}
  & \Rightarrow \text{Area}=3.14\times 42.25 \\
 & \Rightarrow \text{Area}=132.665\text{ c}{{\text{m}}^{2}} \\
\end{align}$
Hence we get the circumference of a circle as 40.82 cm and area of a circle as $132.665\text{ c}{{\text{m}}^{2}}$.

Note: Alternatively we can also use the formula of circumference of a circle in terms of diameter which is given as $\pi d$, where d is the diameter of a circle. To solve such types of questions students must know the basic formulas of geometrical shapes.