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 answer:

V =  73739.4628 cm³

Step-by-step explanation:

$$\begin{gathered} h=18\text{ cm } \\ {D}_1=80\text{ cm } \\ {D}_2=60\text{ cm } \\ {r}_1=D_1\mathrm{/}2=80\mathrm{/}2=40\text{ cm } \\ {r}_2=D_2\mathrm{/}2=60\mathrm{/}2=30\text{ cm } \\ V={\displaystyle \frac{\pi \cdot h}{6}}\cdot (3\cdot r_1^2+3\cdot r_2^2+h^2)={\displaystyle \frac{3.1416\cdot 18}{6}}\cdot (3\cdot 40^2+3\cdot 30^2+18^2)=73739.4628{\text{cm}}^3=7.374\cdot 10^4{\text{cm}}^3 \end{gathered}$$

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