Question

Find the area of the sector in radians whose central angle is ${{45}^{\circ }}$ and radius is $2$.

Answer 1

Hint: We have a direct formula to find the area of the sector. We have to just put the values in that formulae and find the answer. One important point in the question is that they asked about the area in radians and hence we also need to convert the area in the required unit. Formula to find the area of the sector is $Area=\dfrac{\theta }{360}\times \pi {{r}^{2}}$.

Complete step-by-step answer:
Finding the area of the sector.
We need to find the area of the sector in radians.
Central angle is ${{45}^{\circ }}$
Radius is $2$
As we know that sector is a small part of the circle and hence we have a direct formula to get the area of the sector.
The formulae is:
$Area=\dfrac{\theta }{360}\times \pi {{r}^{2}}$
We can put the values in the above formula.
$\begin{align}
  & Area=\dfrac{45}{360}\times \pi \times 4 \\
 & Area=\dfrac{\pi }{2} \\
\end{align}$
As we can see that the area we found here is already in radians and hence no need to convert .

Therefore the area of the sector is $\dfrac{\pi }{2}$.

Note: The major point in the question is the unit of the area. We can find the area of the sector in the form of a metric unit using the decimal value of pi. One other method to do this question is to use different values of pie and then just convert the area we found in the radians form. In that method we need some extra calculation and hence we can use the method which is provided above to be more efficient. While doing these types of questions we should always take care of the units we are using.