Calculate the cylinder

Calculate the volume of a cylinder, given:
S = 144π cm²
height = 6 cm

Final Answer:

V = 678.584 cm³

S = 144 π = 144 \cdot 3.1416 ≐ 452.3893 cm^{2} h = 6 cm S = 2 π r^{2} + 2 π \cdot r \cdot h S = 2 \cdot p i \cdot r^{2} + 2 \cdot p i \cdot r \cdot h 452.38934211693 = 2 \cdot 3.1415926 \cdot r^{2} + 2 \cdot 3.1415926 \cdot r \cdot 6 - 6.2831852 r^{2} - 37.699 r + 452.389 = 0 6.2831852 r^{2} + 37.699 r - 452.389 = 0 a = 6.283185; b = 37.699; c = - 452.389 D = b^{2} - 4 a c = 37.69 9^{2} - 4 \cdot 6.283185 \cdot (- 452.389) = 12791.007061377 D > 0 r_{1, 2} = \frac{- b \pm D}{2 a} = \frac{- 3 7 . 7 \pm 1 2 7 9 1 . 0 1}{1 2 . 5 6 6 3 7} r_{1, 2} = - 3 \pm 9 r_{1} = 6.000000068 r_{2} = - 12.000000068 r = r_{1} = 6 cm S_{1} = π \cdot r^{2} = 3.1416 \cdot 6^{2} ≐ 113.0973 cm^{2} V = S_{1} \cdot h = 113.0973 \cdot 6 ≐ 678.584 cm^{3} Verifying Solution: S_{2} = 2 \cdot S_{1} + 2 π \cdot r \cdot h = 2 \cdot 113.0973 + 2 \cdot 3.1416 \cdot 6 \cdot 6 ≐ 452.3893 cm^{2} S_{2} = S

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