Spherical segment

Calculate the volume of a spherical segment 18 cm high. The diameter of the lower base is 80 cm, the upper base 60 cm.

Correct result:

V =  73739.463 cm3

Solution:

h=18 cm D1=80 cm D2=60 cm  r1=D1/2=80/2=40 cm r2=D2/2=60/2=30 cm  V=π⋅ h6⋅ (3⋅ r12+3⋅ r22+h2)=3.1416⋅ 186⋅ (3⋅ 402+3⋅ 302+182)=73739.463 cm3h=18 \ \text{cm} \ \\ D_{1}=80 \ \text{cm} \ \\ D_{2}=60 \ \text{cm} \ \\ \ \\ r_{1}=D_{1}/2=80/2=40 \ \text{cm} \ \\ r_{2}=D_{2}/2=60/2=30 \ \text{cm} \ \\ \ \\ V=\dfrac{ \pi \cdot \ h }{ 6 } \cdot \ (3 \cdot \ r_{1}^2+3 \cdot \ r_{2}^2+h^2)=\dfrac{ 3.1416 \cdot \ 18 }{ 6 } \cdot \ (3 \cdot \ 40^2+3 \cdot \ 30^2+18^2)=73739.463 \ \text{cm}^3

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