Cylinder surface area

Volume of a cylinder whose height is equal to the radius of the base is 678.5 dm3. Calculate its surface area.

Result

S =  452.352 dm2

Solution:

V=678.5 h=r V=πr2 h=πr3 r=V/π3=678.5/3.14163≐5.9998 h=r=5.9998≐5.9998 S=2π⋅ r2+2π⋅ r⋅ h=2⋅ 3.1416⋅ 5.99982+2⋅ 3.1416⋅ 5.9998⋅ 5.9998≐452.352=452.352 dm2V = 678.5 \ \\ h = r \ \\ V = \pi r^2 \ h = \pi r^3 \ \\ r = \sqrt[3]{ V/\pi} = \sqrt[3]{ 678.5/3.1416} \doteq 5.9998 \ \\ h = r = 5.9998 \doteq 5.9998 \ \\ S = 2 \pi \cdot \ r^2 + 2 \pi \cdot \ r \cdot \ h = 2 \cdot \ 3.1416 \cdot \ 5.9998^2 + 2 \cdot \ 3.1416 \cdot \ 5.9998 \cdot \ 5.9998 \doteq 452.352 = 452.352 \ dm^2

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