The cone - S,V

Calculate the volume and surface area of the cone if its radius r = 6 cm and side s = 10 cm.

Correct result:

V =  301.5929 cm³
S =  301.5929 cm²

Solution:

$$\begin{gathered} s=10\text{ cm } \\ r=6\text{ cm } \\ {s}^2=r^2+h^2 \\ h=\sqrt{s^2-r^2}=\sqrt{10^2-6^2}=8\text{ cm } \\ {S}_1=\pi \cdot r^2=3.1416\cdot 6^2\doteq 113.0973{\text{cm}}^2 \\ V={\displaystyle \frac{1}{3}}\cdot S_1\cdot h={\displaystyle \frac{1}{3}}\cdot 113.0973\cdot 8=301.5929{\text{cm}}^3 \end{gathered}$$

$$\begin{gathered} s=\sqrt{r^2+h^2}=\sqrt{6^2+8^2}=10\text{ cm } \\ {S}_2=\pi \cdot r\cdot s=3.1416\cdot 6\cdot 10\doteq 188.4956 \\ S=S_1+S_2=113.0973+188.4956=301.5929{\text{cm}}^2 \end{gathered}$$

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