Find the area of the corresponding major sector of a circle of radius 28 𝑐𝑚 and the central angle 45°.

We have been given the radius of a circle and the central angle. We have to find the corresponding area of major sector.

It can be said that 𝐴𝑟𝑒𝑎 𝑜𝑓 𝑚𝑎𝑗𝑜𝑟 𝑠𝑒𝑐𝑡𝑜𝑟 = 𝐴𝑟𝑒𝑎 𝑜𝑓 𝑐𝑖𝑟𝑐𝑙𝑒 − 𝐴𝑟𝑒𝑎 𝑜𝑓 𝑚𝑖𝑛𝑜𝑟 𝑠𝑒𝑐𝑡𝑜r

Area of circle = π𝑟²

^{Now, area of minor sector is given by the formula =} $\pi r^2\times \frac{\theta }{{360}^{\circ }}$

^{where θ is the central of  the sector.}

Therefore, 𝐴𝑟𝑒𝑎 𝑜𝑓 𝑚𝑎𝑗𝑜𝑟 𝑠𝑒𝑐𝑡𝑜𝑟 =  $\pi r^2-\left(\pi r^2\times \frac{\theta }{{360}^{\circ }}\right)$

$\begin{array}{r}\Rightarrow \text{ Area }=\pi r^2\left(1-\frac{\theta }{{360}^{\circ }}\right)\\ \Rightarrow \text{ Area }=\frac{22}{7}\times {28}^2\times \left(1-\frac{45}{360}\right)\\ \Rightarrow \text{ Area }=\frac{22}{7}\times {28}^2\times \left(1-\frac{7}{8}\right)\\ \Rightarrow \text{ Area }=2156{\mathrm{cm}}^2\end{array}$

Therefore, area of major sector is 2156 𝑐𝑚² .