Question

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

Answer 1

We know that

Diameter of the flower bed$=66m$

Radius of the flower bed $=\frac{d}{2}=\frac{66}{2}=33m$

Area of flower bed $=\pi r^2$

$$\begin{gathered} =3.14\times {33}^2 \\ =3.14\times 1089 \\ =3419.46m^2 \end{gathered}$$

So, radius of flower bed and path together$=33+4=37m$

Area of the flower bed and path together $=\pi r^2$

$$\begin{gathered} =3.14\times {37}^2 \\ =3.14\times 1369 \\ =4298.66m^2 \end{gathered}$$

$\text{Area of the path = Area of the flower bed and path together – Area of flower bed}$

$$\begin{gathered} =4298.66–3419.46 \\ =879.20m^2 \end{gathered}$$

Hence, area of the path $=879.20m^2$