Round flowerbed

Around a round flowerbed with a diameter of 6 meters and I will make a sidewalk up to 0.5 meters wide. How much gravel is needed if the layer is to be 5 cm high?

Correct answer:

V =  0.5105 m³

Step-by-step explanation:

$$\begin{gathered} D=6\text{ m } \\ h=0.5\text{ m } \\ c=5\text{ cm}\to \text{ m}=5\mathrm{/}100\text{ m}=0.05\text{ m } \\ r=D\mathrm{/}2=6\mathrm{/}2=3\text{ m } \\ {r}_2=r+h=3+0.5={\displaystyle \frac{7}{2}}=3.5\text{ m } \\ S=\pi \cdot r_2^2-\pi \cdot r^2=3.1416\cdot 3.5^2-3.1416\cdot 3^2\doteq 10.2102{\text{m}}^2 \\ V=S\cdot c=10.2102\cdot 0.05=0.5105{\text{m}}^3 \end{gathered}$$

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