Hemispherical hollow

The vessel's hemispherical hollow is filled with water to a height of 10 cm =. How many liters of water are inside if the hollow's inside diameter is d = 28cm?

Correct answer:

V =  3.351 l

Step-by-step explanation:

$$\begin{gathered} v=10\text{cm}\to \text{dm}=10:10\text{dm}=1\text{dm} \\ D=28\text{cm}\to \text{dm}=28:10\text{dm}=2.8\text{dm} \\ r=D/2=\frac{14}{5}/2=\frac{14}{5\cdot 2}=\frac{14}{10}=\frac{7}{5}=1.4\text{dm} \\ {r}_1=\sqrt{r^2-(r-v{)}^2}=\sqrt{1.4^2-(1.4-1{)}^2}\doteq 1.3416\text{dm} \\ 1l=1d{m}^3 \\ V=\frac{1}{6}\cdot \pi \cdot v\cdot (3\cdot r_1^2+v^2)=\frac{1}{6}\cdot 3.1416\cdot 1\cdot (3\cdot 1.3416^2+1^2)=3.351\text{l} \end{gathered}$$

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