Surface of the cone

Calculate the surface of the cone if its height is 8 cm and the volume is 301.44 cm³.

Correct answer:

S =  301.4706 cm²

Step-by-step explanation:

$$\begin{gathered} h=8\text{ cm } \\ V=301.44{\text{cm}}^3 \\ V={\displaystyle \frac{1}{3}}\cdot S_1\cdot h \\ {S}_1={\displaystyle \frac{3\cdot V}{h}}={\displaystyle \frac{3\cdot 301.44}{8}}={\displaystyle \frac{2826}{25}}=113.04{\text{cm}}^2 \\ {S}_1=\pi r^2 \\ r=\sqrt{S_1\mathrm{/}\pi }=\sqrt{113.04\mathrm{/}3.1416}\doteq 5.9985\text{ cm } \\ s=\sqrt{r^2+h^2}=\sqrt{5.9985^2+8^2}\doteq 9.9991\text{ cm } \\ {S}_2=\pi \cdot r\cdot s=3.1416\cdot 5.9985\cdot 9.9991\doteq 188.4306{\text{cm}}^2 \\ S=S_1+S_2=113.04+188.4306=301.4706{\text{cm}}^2 \end{gathered}$$

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