# Cylinder diameter

The surface of the cylinder is 149 cm2. The cylinder height is 6 cm. What is the diameter of this cylinder?

Correct result:

D =  5.439 cm

#### Solution:

$S = 2\pi r^2 + 2\pi r h \ \\ S = \pi D^2/2 + \pi D h \ \\ \ \\ \pi D^2/2 + \pi D h - S = 0 \ \\ \pi D^2/2 + \pi \cdot 6 \cdot D - 149 = 0 \ \\ \ \\ 1.5707963267949D^2 +18.85D -149 =0 \ \\ \ \\ a=1.5707963267949; b=18.85; c=-149 \ \\ D = b^2 - 4ac = 18.85^2 - 4\cdot 1.5707963267949 \cdot (-149) = 1291.500369209 \ \\ D>0 \ \\ \ \\ D_{1,2} = \dfrac{ -b \pm \sqrt{ D } }{ 2a } = \dfrac{ -18.85 \pm \sqrt{ 1291.5 } }{ 3.1415926535898 } \ \\ D_{1,2} = -6 \pm 11.43924587037 \ \\ D_{1} = 5.4392458703697 \ \\ D_{2} = -17.43924587037 \ \\ \ \\ \text{ Factored form of the equation: } \ \\ 1.5707963267949 (D -5.4392458703697) (D +17.43924587037) = 0 \ \\ \ \\ D>0 \ \\ D \doteq 5.439 \ \text{cm}$

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