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=75=1.4 dm r1=r2−(r−v)2=1.42−(1.4−1)2≐1.3416 dm  1 l=1dm3 V=16⋅ π⋅ v⋅ (3⋅ r12+v2)=16⋅ 3.1416⋅ 1⋅ (3⋅ 1.34162+12)≐3.351=3.351  l 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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