Calculate 81034

Calculate the volume of the spherical segment and the surface area of the canopy if the radius of the sphere is r=5cm and the radius of the circular base of the segment ρ=4cm.

Correct answer:

V =  54.4543 cm³
S =  62.8319 cm²

Step-by-step explanation:

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

$S=2\pi \cdot r\cdot h=2\cdot 3.1416\cdot 5\cdot 2=62.8319{\text{cm}}^2$

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