Spherical cap

Calculate the volume of the spherical cap and the areas of the spherical canopy if r = 5 cm (radius of the sphere), ρ = 4 cm (radius of the circle of the cap).

Correct answer:

V =  54.4543 cm³
S =  113.0973 cm²

Step-by-step explanation:

$$\begin{gathered} r=5\text{cm} \\ \rho =4\text{cm} \\ {r}^2=(r-v{)}^2+{\rho }^2 \\ h=r-\sqrt{r^2-{\rho }^2}=5-\sqrt{5^2-4^2}=2\text{cm} \\ V=\frac{\pi \cdot h}{6}\cdot (3\cdot {\rho }^2+h^2)=\frac{3.1416\cdot 2}{6}\cdot (3\cdot 4^2+2^2)=54.4543{\text{cm}}^3 \end{gathered}$$

$S=2\pi \cdot r\cdot h+\pi \cdot {\rho }^2=2\cdot 3.1416\cdot 5\cdot 2+3.1416\cdot 4^2=113.0973{\text{cm}}^2$

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