Surface of the cylinder

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

Correct result:

S =  70.053 dm2

Solution:

V=45 l=πr2h 2πr=3h h=23πr V=23π2r3 r=3V2π23=1.9 dm h=23πr=3.98 dm S=2πr2+2πrh=2π⋅1.92+2π⋅1.9⋅3.98=70.053 dm2V = 45 \ l = \pi r^2 h \ \\ 2 \pi r = 3 h \ \\ h = \dfrac23 \pi r \ \\ V = \dfrac23 \pi^2r^3 \ \\ r = \sqrt[3]{\dfrac{ 3V}{ 2 \pi^2}} = 1.9 \ dm \ \\ h = \dfrac23 \pi r = 3.98 \ dm \ \\ S = 2 \pi r^2 + 2\pi r h = 2 \pi \cdot 1.9^2 + 2\pi \cdot 1.9 \cdot 3.98 = 70.053 \ \text{dm}^2

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