# 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 result:

V =  0.511 m3

#### Solution:

$D=6 \ \text{m} \ \\ h=0.5 \ \text{m} \ \\ c=5 \ cm \rightarrow m=5 / 100 \ m=0.05 \ m \ \\ \ \\ r=D/2=6/2=3 \ \text{m} \ \\ r_{2}=r+h=3+0.5=\dfrac{ 7 }{ 2 }=3.5 \ \text{m} \ \\ \ \\ S=\pi \cdot \ r_{2}^2 - \pi \cdot \ r^2=3.1416 \cdot \ 3.5^2 - 3.1416 \cdot \ 3^2 \doteq 10.2102 \ \text{m}^2 \ \\ \ \\ V=S \cdot \ c=10.2102 \cdot \ 0.05=0.511 \ \text{m}^3$

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