Hemispherical hollow

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

Correct result:

V =  3.351 l

Solution:

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

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