Surface of the cylinder

Calculate the cylinder's surface area when its volume is 45 l, and the base's perimeter is three times the height.

Final Answer:

S =  70.0527 dm2

Step-by-step explanation:

V=45 l→ dm3=45⋅ 1  dm3=45 dm3 o=3h 2 π r = 3 h h = 32​ π r V = π r 2 h =  π r 2  32​ π r V = π r 2 h =  π2 r3  32​  r=32π23⋅ V​​=32⋅ 3.141623⋅ 45​​≐1.8982 dm h=32​⋅ π⋅ r=32​⋅ 3.1416⋅ 1.8982≐3.9755 dm  S=2π⋅ r2+2π⋅ r⋅ h=2⋅ 3.1416⋅ 1.89822+2⋅ 3.1416⋅ 1.8982⋅ 3.9755≐70.0527 dm2   Verifying Solution:   V2​=π⋅ r2⋅ h=3.1416⋅ 1.89822⋅ 3.9755=45 l

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