Question

To the nearest pound, how much grain with the Silo hold if the height of the ladder is 40 feet and the radius is 6 feet? (1 cubic foot = 62.43 pounds)

Answer 1

Question #53951– Math – Geometry

To the nearest pound, how much grain with the Silo hold if the height of the ladder is 40 feet and the radius is 6 feet? (1 cubic foot = 62.43 pounds)

$h = 40$ feet, $r = 6$ feet

Solution:

The Silo is a composite of cylinder and hemisphere.

$$V _ {c} = \pi r ^ {2} h = \pi \cdot 6 ^ {2} \cdot 4 0 = 4, 5 2 3. 8 9 \text{ cubic foot} = 2 8 2, 4 2 6. 6 7 \text{ pounds}$$ $$V _ {h} = \frac {1}{2} \cdot \frac {4}{3} \pi r ^ {3} = \pi \cdot \frac {2}{3} \cdot 6 ^ {3} = 4 5 2. 3 9 \text{ cubic foot} = 2 8, 2 4 2. 6 7 \text{ pounds}$$ $$V = V _ {c} + V _ {h} = 2 8 2, 4 2 6. 6 7 + 2 8, 2 4 2. 6 7 = 3 1 0, 6 6 9 \text{ pounds}$$

Answer:

310,669 pounds grain.

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