Spherical sector

Calculate the volume and surface area of ​​a spherical sector if the spherical segment that is part of the sector has a base radius r1 = 6 cm and a height v = 2 cm.

Correct answer:

V =  418.879 cm³
S =  125.6637 cm²

Step-by-step explanation:

$$\begin{gathered} r_1=6\text{cm} \\ v=2\text{cm} \\ {r}_1^2=v(2r-v) \\ {r}_1^2=2rv-v^2 \\ r=\frac{r_1^2+v^2}{2\cdot v}=\frac{6^2+2^2}{2\cdot 2}=10\text{cm} \\ V=\frac{2}{3}\cdot \pi \cdot r^2\cdot v=\frac{2}{3}\cdot 3.1416\cdot 10^2\cdot 2=418.879{\text{cm}}^3 \end{gathered}$$

$S=2\pi \cdot r\cdot v=2\cdot 3.1416\cdot 10\cdot 2=125.6637{\text{cm}}^2$

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