Bottles of juice

How many 2-liter bottles of juice need to buy if you want to transfer the juice to 50 pitchers' rotary cone shape with a diameter of 24 cm and a base side length of 1.5 dm?

Correct answer:

n =  72.4

Step-by-step explanation:

$$\begin{gathered} D=24\text{cm}\to \text{dm}=24:10\text{dm}=2.4\text{dm} \\ s=1.5\text{dm} \\ {V}_1=2\text{l} \\ r=D/2=2.4/2=\frac{6}{5}=1\frac{1}{5}=1.2\text{dm} \\ {h}^2=s^2+r^2 \\ h=\sqrt{s^2+r^2}=\sqrt{1.5^2+1.2^2}\doteq 1.9209\text{dm} \\ {V}_2=\frac{1}{3}\cdot \pi \cdot r^2\cdot h=\frac{1}{3}\cdot 3.1416\cdot 1.2^2\cdot 1.9209\doteq 2.8967{\text{dm}}^3 \\ {V}_3=50\cdot V_2=50\cdot 2.8967\doteq 144.8353{\text{dm}}^3 \\ n=\frac{V_3}{V_1}=\frac{144.8353}{2}=72.4 \end{gathered}$$

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