Cylinder - area

The diameter of the cylinder is one-third the length of the height of the cylinder. Calculate the surface of cylinder if its volume is 2 m3.

Result

S =  9.857 m2

Solution:

V=2m3=πr2h 2r=h/3 h=6r V=6πr3 r=V6π3=0.47 m h=6r=2.84 m S=2πr2+2πrh=2π0.472+2π0.472.84=9.857 m2V = 2 m^3 = \pi r^2 h \ \\ 2 r = h/3 \ \\ h = 6 r \ \\ V = 6 \pi r^3 \ \\ r = \sqrt[3]{\dfrac{ V}{ 6 \pi}} = 0.47 \ m \ \\ h = 6 r = 2.84 \ m \ \\ S = 2 \pi r^2 + 2\pi r h = 2 \pi \cdot 0.47^2 + 2\pi \cdot 0.47 \cdot 2.84 = 9.857 \ m^2



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