Question

The area of a circular pond is 1 acre find the cost of gravelling a path 4 ft wide around it at $ 1 per square ft
1 acre=4840 sq. yard

Answer 1

Answer :

Given : The area of circular pond = 1 acre
And
We know
1 acre = 4840 square yard
And
1 square yard = 9 square foot
So,
4840 square yard = 9 $\times$ 4840 = 43560 square foot
Let radius of pond = r ft
And
We know area of circle = ${\mathrm{\pi r}}^2$ , So we get

$$\begin{gathered} \Rightarrow {\mathrm{\pi r}}^2=43560 \\ \Rightarrow \frac{22r^2}{7}=43560 \\ \Rightarrow \frac{r^2}{7}=1980 \\ \Rightarrow r^2=13860 \\ \Rightarrow r^{}=117.728\approx \mathbf{117}\mathbf{.}\mathbf{73}\mathbf{}\mathit{f}\mathit{t} \end{gathered}$$
So,
Radius of pond including 4 ft wide path around it = 117.73 + 4 = 121.73 ft
So,
Area of path = Area of circular pond with path - Area of circular pond

Area of circular pond with path = $\frac{22}{7}\times 121.73\times 121.73=\frac{326000.2438}{7}=\mathbf{46571}\mathbf{.}\mathbf{46}\mathbf{}\mathit{f}{\mathit{t}}^{\mathbf{2}}$
So,
Area of path = 46571.46 - 43560 = 3011.46 square ft
And
Rate of gravelling the path = $1 per square ft
So,
Cost of gravelling the path = 1 $\times$ 3011.46 = $ 3011.46 ( Ans )