Glass cocktail level

The cone-shaped glass has a volume of 2.5 dl and a diameter of 13 cm. How much cocktail is left in the glass if the level only reaches half the height of the glass?

Final Answer:

V₂ =  0.31 dl

Step-by-step explanation:

$$\begin{gathered} d=13\text{cm} \\ V=2.5\text{dl}\to {\text{cm}}^3=2.5\cdot 100{\text{cm}}^3=250{\text{cm}}^3 \\ r=d/2=13/2=\frac{13}{2}=6.5\text{cm} \\ {S}_1=\pi \cdot r^2=3.1416\cdot 6.5^2\doteq 132.7323{\text{cm}}^2 \\ V=\frac{1}{3}\cdot S_1\cdot h \\ h=3\cdot V/S_1=3\cdot 250/132.7323\doteq 5.6505\text{cm} \\ {h}_2=h/2=5.6505/2\doteq 2.8252\text{cm} \\ r:h=r_2:h_2 \\ {r}_2=r\cdot \frac{h_2}{h}=6.5\cdot \frac{2.8252}{5.6505}=\frac{13}{4}=3.25\text{cm} \\ {S}_2=\pi \cdot r_2^2=3.1416\cdot 3.25^2\doteq 33.1831{\text{cm}}^2 \\ {V}_1=\frac{1}{3}\cdot S_2\cdot h_2=\frac{1}{3}\cdot 33.1831\cdot 2.8252=\frac{125}{4}=31.25{\text{cm}}^3 \\ {V}_2=V_1\to \text{dl}=V_1:100\text{dl}=31.25:100\text{dl}=0.31\text{dl}=0.31\text{dl} \end{gathered}$$

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