A goat 2

As shown, a goat is tied at one corner of a rectangular shed by a 5-meter-long rope. The shed measures 3 m by 2 m and is surrounded by grassland. What is the area of the grassland in which the goat can graze? Give your answer to the nearest m².

Final Answer:

A =  69 m²

Step-by-step explanation:

$$\begin{gathered} r=5\text{m} \\ a=3\text{m} \\ b=2\text{m} \\ {S}_1=\frac{3}{4}\cdot \pi \cdot r^2=\frac{3}{4}\cdot 3.1416\cdot 5^2\doteq 58.9049{\text{m}}^2 \\ {r}_2=r-a=5-3=2\text{m} \\ {r}_3=r-b=5-2=3\text{m} \\ {S}_2=\frac{1}{4}\cdot \pi \cdot r_2^2=\frac{1}{4}\cdot 3.1416\cdot 2^2\doteq 3.1416{\text{m}}^2 \\ {S}_3=\frac{1}{4}\cdot \pi \cdot r_3^2=\frac{1}{4}\cdot 3.1416\cdot 3^2\doteq 7.0686{\text{m}}^2 \\ A=S_1+S_2+S_3=58.9049+3.1416+7.0686=69{\text{m}}^2 \end{gathered}$$

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