Spherical tank

The tank of a water tower is a sphere of radius 35ft. If the tank is filled to one quarter of full, what is the height of the water?

Correct result:

h = 22.8446 ft

Solution:

r = 35 ft V = \frac{4}{3} \cdot π \cdot r^{3} = \frac{4}{3} \cdot 3.1416 \cdot 3 5^{3} ≐ 179594.38 {ft}^{3} V_{1} = \frac{1}{4} \cdot V = \frac{1}{4} \cdot 179594.38 ≐ 44898.595 {ft}^{3} V_{2} = \frac{π \cdot h^{2}}{3} (3 r - h) V_{1} = V_{2} \frac{π \cdot r^{3}}{3} = \frac{π \cdot h^{2}}{3} (3 r - h) r^{3} = h^{2} (3 r - h) 42875 = (105 - h) h^{2} h^{3} - 105 h^{2} + 42875 = 0 h_{1} = - 18.6231 h_{2} = 22.8446 h_{3} = 100.778 0 < h < 2 r h = h_{2} = 22.8446 = 22.8446 ft Verifying Solution: V_{2} = \frac{π \cdot h^{2}}{3} \cdot (3 \cdot r - h) = \frac{3.1416 \cdot 22.844 6^{2}}{3} \cdot (3 \cdot 35 - 22.8446) ≐ 44898.5017 {ft}^{3}

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Showing 1 comment:

Math student

ca you show me the step by step of the height

1 month ago 2 Likes Like

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