Equilateral cylinder

Equilateral cylinder (height = base diameter; h = 2r) has a volume of V = 199 cm³ . Calculate the surface area of the cylinder.

Correct result:

S =  188.69 cm²

Solution:

$$\begin{gathered} V=199{\text{cm}}^3 \\ h=2r \\ V=\pi \cdot r^2\cdot h=2\pi r^3 \\ r=\sqrt[3]{{\displaystyle \frac{V}{2\pi }}}=\sqrt[3]{{\displaystyle \frac{199}{2\cdot 3.1416}}}\doteq 3.1639\text{ cm } \\ h=2\cdot r=2\cdot 3.1639\doteq 6.3278\text{ cm } \\ {S}_1=\pi \cdot r^2=3.1416\cdot 3.1639^2\doteq 31.4484{\text{cm}}^2 \\ {V}_1=S_1\cdot h=31.4484\cdot 6.3278=199{\text{cm}}^3 \\ {V}_1=V \\ S=2\cdot S_1+2\pi \cdot r\cdot h=2\cdot 31.4484+2\cdot 3.1416\cdot 3.1639\cdot 6.3278=188.69{\text{cm}}^2 \end{gathered}$$

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