# 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:

$V=199 \ \text{cm}^3 \ \\ h=2r \ \\ V=\pi \cdot \ r^2 \cdot \ h=2 \ \pi r^3 \ \\ r=\sqrt[3]{ \dfrac{ V }{ 2 \pi } }=\sqrt[3]{ \dfrac{ 199 }{ 2 \cdot \ 3.1416 } } \doteq 3.1639 \ \text{cm} \ \\ h=2 \cdot \ r=2 \cdot \ 3.1639 \doteq 6.3278 \ \text{cm} \ \\ \ \\ S_{1}=\pi \cdot \ r^2=3.1416 \cdot \ 3.1639^2 \doteq 31.4484 \ \text{cm}^2 \ \\ \ \\ V_{1}=S_{1} \cdot \ h=31.4484 \cdot \ 6.3278=199 \ \text{cm}^3 \ \\ V_{1}=V \ \\ \ \\ S=2 \cdot \ S_{1} + 2 \pi \cdot \ r \cdot \ h=2 \cdot \ 31.4484 + 2 \cdot \ 3.1416 \cdot \ 3.1639 \cdot \ 6.3278=188.69 \ \text{cm}^2$

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