Determine 73454

The volume of the cut cone is V = 38000π cm³. The radius of the lower base is 10 cm larger than the radius of the upper base. Determine the radius of the base if height v = 60 cm.

Correct answer:

r₁ = 20 cm
r₂ = 30 cm

Step-by-step explanation:

V = 38000 π = 38000 \cdot 3.1416 ≐ 119380.5208 cm^{3} v = 60 cm r_{2} = 10 + r_{1} V = \frac{1}{3} π \cdot v \cdot (r_{1}^{2} + r_{1} \cdot r_{2} + r_{2}^{2}) V = p i / 3 \cdot v \cdot (x^{2} + x \cdot (10 + x) + (10 + x)^{2}) 119380.52083641 = 3.1415926 / 3 \cdot 60 \cdot (x^{2} + x \cdot (10 + x) + (10 + x)^{2}) - 188.49555599999 x^{2} - 1884.956 x + 113097.336 = 0 188.49555599999 x^{2} + 1884.956 x - 113097.336 = 0 a = 188.495556; b = 1884.956; c = - 113097.336 D = b^{2} - 4 a c = 1884.95 6^{2} - 4 \cdot 188.495556 \cdot (- 113097.336) = 88826438.114787 D > 0 x_{1, 2} = \frac{- b \pm D}{2 a} = \frac{- 1 8 8 4 . 9 6 \pm 8 8 8 2 6 4 3 8 . 1 1}{3 7 6 . 9 9 1 1 1 2} x_{1, 2} = - 5 \pm 25 x_{1} = 20.000000216 x_{2} = - 30.000000216 r_{1} = x_{1} = 20 = 20 cm

Our quadratic equation calculator calculates it.

r_{2} = 10 + r_{1} = 10 + 20 = 30 = 30 cm Verifying Solution: V_{2} = \frac{1}{3} \cdot π \cdot v \cdot (r_{1}^{2} + r_{1} \cdot r_{2} + r_{2}^{2}) = \frac{1}{3} \cdot 3.1416 \cdot 60 \cdot (2 0^{2} + 20 \cdot 30 + 3 0^{2}) ≐ 119380.5208 cm^{3}

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Determine 73454

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