Equilateral cylinder

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

Result

S =  188.69 cm2

Solution:

V=199 cm3 h=2r V=π⋅ r2⋅ h=2 πr3 r=V2π3=1992⋅ 3.14163≐3.1639 cm h=2⋅ r=2⋅ 3.1639≐6.3278 cm  S1=π⋅ r2=3.1416⋅ 3.16392≐31.4484 cm2  V1=S1⋅ h=31.4484⋅ 6.3278=199 cm3 V1=V  S=2⋅ S1+2π⋅ r⋅ h=2⋅ 31.4484+2⋅ 3.1416⋅ 3.1639⋅ 6.3278≐188.6905≐188.69 cm2V=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 \doteq 188.6905 \doteq 188.69 \ \text{cm}^2

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