The cylinder

The cylinder has a surface area of 300 square meters, while the cylinder's height is 12 m. Calculate the volume of this cylinder.

Correct answer:

V = 374.3807 m³

Step-by-step explanation:

S = 300 m^{2} h = 12 cm S = 2 * p i * r^{2} + 2 * p i * r * h 300 = 2 \cdot 3.1415926 \cdot r^{2} + 2 \cdot 3.1415926 \cdot r \cdot 12 - 6.283185 r^{2} - 75.398 r + 300 = 0 6.283185 r^{2} + 75.398 r - 300 = 0 a = 6.283185; b = 75.398; c = - 300 D = b^{2} - 4 a c = 75.39 8^{2} - 4 \cdot 6.283185 \cdot (- 300) = 13224.71394108 D > 0 r_{1, 2} = \frac{- b \pm D}{2 a} = \frac{- 7 5 . 4 \pm 1 3 2 2 4 . 7 1}{1 2 . 5 6 6 3 7} r_{1, 2} = - 6.00000019 \pm 9.1513107014069 r_{1} = 3.151310510421 r_{2} = - 15.151310892393 Factored form of the equation: 6.283185 (r - 3.151310510421) (r + 15.151310892393) = 0 r = r_{1} = 3.1513 ≐ 3.1513 S_{1} = π \cdot r^{2} = 3.1416 \cdot 3.151 3^{2} ≐ 31.1984 m^{2} V = S_{1} \cdot h = 31.1984 \cdot 12 ≐ 374.3807 m^{3} Verifying Solution: S_{2} = 2 π \cdot r^{2} + 2 π \cdot r \cdot h = 2 \cdot 3.1416 \cdot 3.151 3^{2} + 2 \cdot 3.1416 \cdot 3.1513 \cdot 12 = 300 S = S_{2}

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