Question

Question 13
A circular flower bed is surrounded by a path 4 m wide. The diameter of the flower bed is 66 m. What is the area of this path? $(Take\pi =3.14)$

Answer 1

Diameter of the circular flower bed = 66 m
$\therefore$ Radius of circular flower bed (r) = $\frac{66}{2}=33m$
$\therefore$ Radius of circular flower bed with 4m wide path (R) = 33 + 4 = 37 m
According to the question,
Area of path = Area of bigger circle = Area of smaller circle
$\Rightarrow \pi R^2-\pi r^2=\pi (R^2-r^2)$
$=\pi \left[\right(37{)}^2-\left(33{)}^2\right]$
$=3.14\left[\right(37+33\left)\right(37-33\left)\right]$ $[\because a^2-b^2=(a+b\left)\right(a-b\left)\right]$
$=3.14\times 70\times 4$
$=879.20m^2$
Therefore, the area of the path is 879.20 $m^2$.