Cone container

The Rotary cone-shaped container has a volume of 1000 cubic cm and a height of 12 cm. Calculate how much metal we need to make this package.

Correct answer:

S =  669.0434 cm²

Step-by-step explanation:

$$\begin{gathered} V=1000{\text{cm}}^3 \\ h=12\text{cm} \\ V=\frac{1}{3}\pi r^{2}h \\ r=\sqrt{3\cdot V/h/\pi }=\sqrt{3\cdot 1000/12/3.1416}\doteq 8.9206\text{cm} \\ s=\sqrt{r^2+h^2}=\sqrt{8.9206^2+12^2}\doteq 14.9525\text{cm} \\ {S}_1=\pi \cdot r^2=3.1416\cdot 8.9206^2=250{\text{cm}}^2 \\ {S}_2=\pi \cdot r\cdot s=3.1416\cdot 8.9206\cdot 14.9525\doteq 419.0434{\text{cm}}^2 \\ S=S_1+S_2=250+419.0434=669.0434{\text{cm}}^2 \end{gathered}$$

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