Fountain grass seed

How many kg of grass seed should be bought to establish a lawn around a circular fountain with a diameter of 5 m if the lawn is to be 1.5 m wide and 1 g of grass seed is used per 1 dm of the square area?

Final Answer:

m =  3.0631 kg

Step-by-step explanation:

$$\begin{gathered} D=5\text{m} \\ s=1.5\text{m} \\ r=D/2=5/2=\frac{5}{2}=2.5\text{m} \\ {r}_2=r+s=2.5+1.5=4\text{m} \\ {S}_1=\pi \cdot r^2=3.1416\cdot 2.5^2\doteq 19.635{\text{m}}^2 \\ {S}_2=\pi \cdot r_2^2=3.1416\cdot 4^2\doteq 50.2655{\text{m}}^2 \\ {S}_3=S_2-S_1=50.2655-19.635\doteq 30.6305{\text{m}}^2 \\ {S}_4=S_3\to {\text{dm}}^2=S_3\cdot 100{\text{dm}}^2=30.6305\cdot 100{\text{dm}}^2=3063.05284{\text{dm}}^2 \\ \sigma =1{\text{g/dm}}^2 \\ {m}_1=S_4\cdot \sigma =3063.0528\cdot 1\doteq 3063.0528\text{g} \\ m=m_1\to \text{kg}=m_1:1000\text{kg}=3063.0528:1000\text{kg}=3.063\text{kg}=3.0631\text{kg} \end{gathered}$$

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