Tin with oil

Tin with oil has the shape of a rotating cylinder whose height is equal to the diameter of its base. The canned surface is 1884 cm². Calculate how many liters of oil are in the tin.

Correct answer:

V =  6.2784 l

Step-by-step explanation:

$$\begin{gathered} S=1884{\text{cm}}^2\to {\text{dm}}^2=1884:100{\text{dm}}^2=18.84{\text{dm}}^2 \\ S=2\pi r^2+2\pi r(2r)=6\pi r^2 \\ r=\sqrt{\frac{S}{6\pi }}=\sqrt{\frac{18.84}{6\cdot 3.1416}}\doteq 0.9997\text{dm} \\ h=2\cdot r=2\cdot 0.9997\doteq 1.9995\text{dm} \\ 1d{m}^3=1liter \\ V=\pi \cdot r^2\cdot h=3.1416\cdot 0.9997^2\cdot 1.9995=6.2784\text{l} \end{gathered}$$

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