Fountain

Around a circular fountain with a diameter of 2m, there is a 0.5m wide strip of land for planting roses. How many m² of land do roses occupy?

Correct answer:

S =  3.927 m²

Step-by-step explanation:

$$\begin{gathered} d_1=2\text{m} \\ a=0.5\text{m} \\ {r}_1=d_1/2=2/2=1\text{m} \\ {r}_2=r_1+a=1+0.5=\frac{3}{2}=1.5\text{m} \\ {S}_1=\pi \cdot r_1^2=3.1416\cdot 1^2\doteq 3.1416{\text{m}}^2 \\ {S}_2=\pi \cdot r_2^2=3.1416\cdot 1.5^2\doteq 7.0686{\text{m}}^2 \\ S=S_2-S_1=7.0686-3.1416=3.927{\text{m}}^2 \end{gathered}$$

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