# 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?

Result

V =  3.351 l

#### Solution:

$v = 10 \ cm = 10 / 10 \ dm = 1 \ dm \ \\ D = 28 \ cm = 28 / 10 \ dm = 2.8 \ dm \ \\ \ \\ r = D/2 = 2.8/2 = \dfrac{ 7 }{ 5 } = 1.4 \ dm \ \\ r_{ 1 } = \sqrt{ r^2-(r-v)^2 } = \sqrt{ 1.4^2-(1.4-1)^2 } \doteq 1.3416 \ dm \ \\ \ \\ 1 \ l = 1dm^3 \ \\ V = \dfrac{ 1 }{ 6 } \cdot \ \pi \cdot \ v \cdot \ (3 \cdot \ r_{ 1 }^2+v^2) = \dfrac{ 1 }{ 6 } \cdot \ 3.1416 \cdot \ 1 \cdot \ (3 \cdot \ 1.3416^2+1^2) \doteq 3.351 = 3.351 \ \text { l }$

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