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18 February, 01:21

The compression strength of concrete (the maximum pressure that can be exerted on the base of the structure) is 1.7 * 107 Pa. What is the height of the tallest cylindrical concrete pillar with a radius of 46 cm that will not collapse under its own weight?

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  1. 18 February, 01:25
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    Height of cylinder = 679.70 m

    Explanation:

    Compression strength = 1.7 x 10⁷ Pa

    Normal force = Compression strength x Area

    Radius = 46 cm = 0.46 m

    Area of cylinder = π x 0.46² = 0.665 m²

    Normal force = 1.7 x 10⁷ x 0.665 = 1.13 x 10⁷ N

    So weight of cylinder = 1.13 x 10⁷ N

    Density of concrete = 25 kN/m³ = 25000 N/m³

    Volume of cylinder = Base area x Height = 0.665 x h

    Weight of cylinder = 25000 x 0.665 x h

    Equating

    25000 x 0.665 x h = 1.13 x 10⁷

    h = 679.70 m

    Height of cylinder = 679.70 m
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