Cylinder diameter

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

Result

D =  5.439 cm

Solution:

S=2πr2+2πrh S=πD2/2+πDh  πD2/2+πDhS=0 πD2/2+π6D149=0  1.57079632679D2+18.85D149=0  a=1.57079632679;b=18.85;c=149 D=b24ac=18.85241.57079632679(149)=1291.50036921 D>0  D1,2=b±D2a=18.85±1291.53.14159265359 D1,2=6±11.4392458704 D1=5.43924587037 D2=17.4392458704   Factored form of the equation:  1.57079632679(D5.43924587037)(D+17.4392458704)=0  D>0 D5.439 cmS = 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 \ \\ \ \\ 1.57079632679D^2 +18.85D -149 =0 \ \\ \ \\ a=1.57079632679; b=18.85; c=-149 \ \\ D = b^2 - 4ac = 18.85^2 - 4\cdot 1.57079632679 \cdot (-149) = 1291.50036921 \ \\ D>0 \ \\ \ \\ D_{1,2} = \dfrac{ -b \pm \sqrt{ D } }{ 2a } = \dfrac{ -18.85 \pm \sqrt{ 1291.5 } }{ 3.14159265359 } \ \\ D_{1,2} = -6 \pm 11.4392458704 \ \\ D_{1} = 5.43924587037 \ \\ D_{2} = -17.4392458704 \ \\ \ \\ \text{ Factored form of the equation: } \ \\ 1.57079632679 (D -5.43924587037) (D +17.4392458704) = 0 \ \\ \ \\ D>0 \ \\ D \doteq 5.439 \ \text{cm}



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