Circular 72244

How many kg of grass seed must be bought to start a lawn in the shape of a circular section with a radius of r= 15 m and a central angle of 45 degrees if 1 g of grass seed is used per 1 dm of the square area?

Correct answer:

m =  8.8357 kg

Step-by-step explanation:

$$\begin{gathered} r=15\text{m} \\ \phi =45{}^{\circ } \\ {S}_1=\pi \cdot r^2=3.1416\cdot 15^2\doteq 706.8583{\text{m}}^2 \\ {S}_2=\frac{\phi }{360}\cdot S_1=\frac{45}{360}\cdot 706.8583\doteq 88.3573{\text{m}}^2 \\ {S}_3=S_2\to {\text{dm}}^2=S_2\cdot 100{\text{dm}}^2=88.3573\cdot 100{\text{dm}}^2=8835.72934{\text{dm}}^2 \\ \sigma =1{\text{g/dm}}^2 \\ {m}_1=S_3\cdot \sigma =\frac{4276493}{484}\cdot 1=\frac{4276493\cdot 1}{484}=\frac{4276493}{484}\doteq 8835.7293\text{g} \\ m=m_1\to \text{kg}=m_1:1000\text{kg}=8835.7293:1000\text{kg}=8.836\text{kg}=8.8357\text{kg} \end{gathered}$$

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