Rotary cylinder 2

Base circumference of the rotary cylinder has same length as its height. What is the surface area of cylinder if its volume is 250 dm3?

Result

S =  248.64 dm2

Solution:

h=2πr V=πr2h=πr2⋅2πr=2⋅pi2r3=250 r=V2π23=2.33 dm h=2πr=14.65 dm  S=2πr2+2πrh=248.64 dm2h = 2\pi r \ \\ V = \pi r^2 h = \pi r^2 \cdot 2 \pi r = 2 \cdot pi^2 r^3 = 250 \ \\ r = \sqrt[3]{ \dfrac{V}{2\pi^2}} = 2.33 \ dm \ \\ h = 2 \pi r = 14.65 \ dm \ \\ \ \\ S = 2 \pi r ^2 + 2\pi r h = 248.64 \ \text{dm}^2

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