Spherical cap

Place a part of the sphere on a 4.6 cm cylinder so that the surface of this section is 20 cm². Determine the radius r of the sphere from which the spherical cap was cut.

Correct result:

v =  1.384 cm
r =  2.6843 cm

Solution:

$$\begin{gathered} D=4.6\text{ cm } \\ {r}_1=D\mathrm{/}2=4.6\mathrm{/}2={\displaystyle \frac{23}{10}}=2.3\text{ cm } \\ S=20{\text{cm}}^2 \\ S=2\pi r_1\mathrm{.}v \\ v={\displaystyle \frac{S}{2\pi \cdot r_1}}={\displaystyle \frac{20}{2\cdot 3.1416\cdot 2.3}}=1.384\text{ cm} \end{gathered}$$

$$\begin{gathered} r^2=r_1^2+v^2 \\ r=\sqrt{r_1^2+v^2}=\sqrt{2.3^2+1.384^2}=2.6843\text{ cm} \end{gathered}$$

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