Volume of the cone

Calculate the volume of the cone if the content of its base is 78.5 cm² and the content of the shell is 219.8 cm².

Correct result:

V =  342.0868 cm³

Solution:

$$\begin{gathered} S_1=78.5{\text{cm}}^2 \\ {S}_2=219.8{\text{cm}}^2 \\ {S}_1=\pi r^2 \\ r=\sqrt{S_1\mathrm{/}\pi }=\sqrt{78.5\mathrm{/}3.1416}\doteq 4.9987\text{ cm } \\ {S}_2=\pi rs \\ s=S_2\mathrm{/}(\pi \cdot r)=219.8\mathrm{/}(3.1416\cdot 4.9987)\doteq 13.9965\text{ cm } \\ {s}^2=r^2+h^2 \\ h=\sqrt{s^2-r^2}=\sqrt{13.9965^2-4.9987^2}\doteq 13.0734\text{ cm } \\ V={\displaystyle \frac{1}{3}}\cdot S_1\cdot h={\displaystyle \frac{1}{3}}\cdot 78.5\cdot 13.0734=342.0868{\text{cm}}^3 \end{gathered}$$

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