Surface area

The volume of a cone is 1000 cm³ and the content area of the axis cut is 100 cm². Calculate the surface area of the cone.

Correct answer:

S =  711.64 cm²

Step-by-step explanation:

$$\begin{gathered} S_1=100c{m}^2 \\ V=1000c{m}^3 \\ {S}_1={\displaystyle \frac{2rh}{2}} \\ rh=100 \\ h=100\mathrm{/}r \\ V={\displaystyle \frac{1}{3}}\pi r^{2}h \\ V={\displaystyle \frac{1}{3}}\pi r^{2}100\mathrm{/}r \\ V={\displaystyle \frac{100}{3}}\pi r \\ r=9.55cm \\ h=100\mathrm{/}r=10.47cm \\ s=\sqrt{r^2+h^2}=14.17cm \\ S=\pi r(r+s)=\pi 9.55\cdot (9.55+14.17)=711.64{\text{cm}}^2 \end{gathered}$$

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