Question

The diagram shows a sand pit in a child's play area. The shape of the sand pit is a sector of a circle of radius 2.25m and sector angle ${56}^0$ . Calculate the area of the sand pit.

Answer 1

Hint:-Here we use the formula of the area of the sector i.e. ${\displaystyle \frac{\theta }{{360}^0}}\times \pi r^2$. Because here in the figure the shape of the sand pit is in the shape of a sector of a circle.

Complete step-by-step answer:
Given radius of circle, r =2.25m by observing the given figure.
Arc subtends an angle of ${56}^0$ at center.
We know that for finding the area of the sector the formula we used is${\displaystyle \frac{\theta }{{360}^0}}\times \pi r^2$.
Now we simply put the given values in the formula to find out the required area.
So the area of sector$={\displaystyle \frac{\theta }{{360}^0}}\times \pi r^2={\displaystyle \frac{56}{360}}\times {\displaystyle \frac{22}{7}}\times (2.25{)}^2=2.474m^2$.
Therefore the required area of the sand pit is $2.474m^2$.

Note: - Whenever we face such a type of question we simply use the formula to get the answer. And if some time you forgot the formula you can apply a unitary method for solving the question. As you know the total angle at the center of the circle is ${360}^0$. And for that angle we know that the area of the circle is $\pi r^2$. Then for angle $\theta$ we apply a simply unitary method.