Everything 25101

The pot with soup is shaped like a cylinder with a bottom diameter of 20 cm and a height of 24 cm. How many guests will we have enough soup for if the pot is filled to two-thirds of the height and 0.25 l of soup is calculated per person? (pay attention to the radius and diameter; the radius is half the diameter. Pay attention to the units - convert everything to dm, 1 liter = 1 dm³)

Correct answer:

n =  20

Step-by-step explanation:

$$\begin{gathered} D=20\text{cm} \\ h=24\text{cm} \\ r=D/2=20/2=10\text{cm} \\ V=\pi \cdot r^2\cdot h=3.1416\cdot 10^2\cdot 24\doteq 7539.8224{\text{cm}}^3 \\ {V}_2=\frac{2}{3}\cdot V=\frac{2}{3}\cdot \frac{1146053}{152}=\frac{2\cdot 1146053}{3\cdot 152}=\frac{2292106}{456}\doteq 5026.5482{\text{cm}}^3 \\ {V}_1=0.25\text{l}\to {\text{cm}}^3=0.25\cdot 1000{\text{cm}}^3=250{\text{cm}}^3 \\ {n}_1=V_2/V_1=\frac{1146053}{228}/250=\frac{1146053}{228\cdot 250}=\frac{1146053}{57000}\doteq 20.1062 \\ n=\lfloor n_1\rfloor =\lfloor 20.1062\rfloor =20 \end{gathered}$$

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