Calculate 19443

Calculate the height of the cylinder when r = 10 mm and S = 800 mm².
Calculate the radius / r / of the cylinder when the height is 20 mm and S = 1000 mm².

Correct answer:

h₁ = 2.7324 mm
r₂ = 6.0983 mm

Step-by-step explanation:

r_{1} = 10 mm S_{1} = 800 mm^{2} S = 2 π r (r + h) h_{1} = \frac{S _{1}}{2 π \cdot r _{1}} - r_{1} = \frac{8 0 0}{2 \cdot 3 . 1 4 1 6 \cdot 1 0} - 10 = 2.7324 mm

h_{2} = 20 mm S_{2} = 1000 mm^{2} S_{2} = 2 π r_{2} (r_{2} + h_{2}) 1000 = 2 * p i * x (x + 20) 1000 = 2 \cdot 3.1415926 \cdot x (x + 20) - 6.283185 x^{2} - 125.664 x + 1000 = 0 6.283185 x^{2} + 125.664 x - 1000 = 0 a = 6.283185; b = 125.664; c = - 1000 D = b^{2} - 4 a c = 125.66 4^{2} - 4 \cdot 6.283185 \cdot (- 1000) = 40924.106503 D > 0 x_{1, 2} = \frac{- b \pm D}{2 a} = \frac{- 1 2 5 . 6 6 \pm 4 0 9 2 4 . 1 1}{1 2 . 5 6 6 3 7} x_{1, 2} = - 10.00000032 \pm 16.098290506729 x_{1} = 6.0982901884192 x_{2} = - 26.098290825039 Factored form of the equation: 6.283185 (x - 6.0982901884192) (x + 26.098290825039) = 0 r_{2} = x_{1} = 6.0983 ≐ 6.0983 mm Verifying Solution: S_{3} = 2 π \cdot r_{2} \cdot (r_{2} + h_{2}) = 2 \cdot 3.1416 \cdot 6.0983 \cdot (6.0983 + 20) = 1000 cm^{2} S_{3} = S_{2}

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