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 lv=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 \ \text{dm} \ \\ r_{1}=\sqrt{ r^2-(r-v)^2 }=\sqrt{ 1.4^2-(1.4-1)^2 } \doteq 1.3416 \ \text{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 \doteq 3.351 \ \text{l}

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