The volume

The volume of the cone is 94.2dm³, the radius of the base is 6 dm Calculate the surface of the cone.

Correct answer:

S =  235.6103 dm²

Step-by-step explanation:

$$\begin{gathered} V=94.2{\text{dm}}^3 \\ r=6\text{ dm } \\ {S}_1=\pi \cdot r^2=3.1416\cdot 6^2\doteq 113.0973{\text{dm}}^2 \\ V={\displaystyle \frac{S_1}{3}}\cdot h \\ h=3\cdot V\mathrm{/}{S}_1=3\cdot 94.2\mathrm{/}113.0973\doteq 2.4987\text{ dm } \\ s=\sqrt{h^2+r^2}=\sqrt{2.4987^2+6^2}\doteq 6.4995\text{ dm } \\ {S}_2=\pi \cdot r\cdot s=3.1416\cdot 6\cdot 6.4995\doteq 122.5129{\text{dm}}^2 \\ S=S_1+S_2=113.0973+122.5129=235.6103{\text{dm}}^2 \end{gathered}$$

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