Lake area

At a speed of 4 km/h, we go around the lake, which has the shape of a circle, in 36 minutes. What is the area of the lake? Please result express in hectares.

Final Answer:

S =  45.8366 ha

Step-by-step explanation:

$$\begin{gathered} v=4\text{km/h} \\ t=36\text{min}\to \text{h}=36:60\text{h}=0.6\text{h} \\ s=v\cdot t=4\cdot 0.6=\frac{12}{5}=2.4\text{km} \\ {s}_1=s\to \text{m}=s\cdot 1000\text{m}=2.4\cdot 1000\text{m}=2400\text{m} \\ r=s_1/(2\pi )=2400/(2\cdot 3.1416)\doteq 381.9719\text{m} \\ {S}_1=\pi \cdot r^2=3.1416\cdot 381.9719^2\doteq 458366.2361{\text{m}}^2 \\ S=S_1\to \text{ha}=S_1:10000\text{ha}=458366.2361:10000\text{ha}=45.837\text{ha}=45.8366\text{ha} \end{gathered}$$

Try another example