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 3.141633.1639 cm h=2 r=2 3.16396.3278 cm  S1=π r2=3.1416 3.1639231.4484 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 6.3278188.6905=188.69 cm2V = 199 \ 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 \ cm \ \\ h = 2 \cdot \ r = 2 \cdot \ 3.1639 \doteq 6.3278 \ cm \ \\ \ \\ S_{ 1 } = \pi \cdot \ r^2 = 3.1416 \cdot \ 3.1639^2 \doteq 31.4484 \ cm^2 \ \\ \ \\ V_{ 1 } = S_{ 1 } \cdot \ h = 31.4484 \cdot \ 6.3278 = 199 \ 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 = 188.69 \ cm^2



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