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How many cubic feet of concrete are needed to pour 4 cylindrical pillars 6 feet high with a diameter of 0.75 feet? Round final answer to the nearest thousandth.

Ask by Fleming Mcguire. in the United States
Mar 17,2025

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To find the total cubic feet of concrete needed for 4 cylindrical pillars: 1. **Calculate the radius** of each pillar: \[ r = \frac{0.75}{2} = 0.375 \text{ feet} \] 2. **Determine the volume of one pillar** using the formula for the volume of a cylinder: \[ V = \pi r^2 h = \pi \times (0.375)^2 \times 6 \] \[ V \approx \pi \times 0.140625 \times 6 \approx 2.6516 \text{ cubic feet} \] 3. **Calculate the total volume for all pillars**: \[ V_{\text{total}} = 4 \times 2.6516 \approx 10.6064 \text{ cubic feet} \] 4. **Round the final answer** to the nearest thousandth: \[ \boxed{10.606} \text{ cubic feet} \]

Solución

Let the radius of each cylindrical pillar be \[ r = \frac{0.75}{2} = 0.375 \text{ feet.} \] The volume \(V\) of one cylinder with height \(h = 6\) feet is given by \[ V = \pi r^2 h. \] Substitute the values: \[ V = \pi (0.375)^2 (6). \] First, compute \[ (0.375)^2 = 0.140625. \] Then, \[ 6 \times 0.140625 = 0.84375. \] So, the volume of one pillar is \[ V = \pi \times 0.84375 \approx 2.6516 \text{ cubic feet.} \] Since there are 4 pillars, the total volume is \[ V_{\text{total}} = 4 \times 2.6516 \approx 10.6064 \text{ cubic feet.} \] Rounded to the nearest thousandth, the total volume is \[ \boxed{10.606} \text{ cubic feet.} \]

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Beyond the Answer

To calculate the volume of one cylindrical pillar, use the formula: \( V = \pi r^2 h \). The radius \( r \) is half of the diameter, which is \( 0.75/2 = 0.375 \) feet. Thus, the volume of one pillar is \( V = \pi (0.375)^2 (6) \approx 2.645 \) cubic feet. For 4 pillars, the total volume is \( 4 \times 2.645 \approx 10.58 \) cubic feet. Rounding to the nearest thousandth, you'll need approximately **10.580 cubic feet** of concrete. Concrete structures, like your cylindrical pillars, can be seen all around—from buildings to bridges! The beauty of concrete is its versatility: it can be molded into various shapes and provides strong support. When calculating volume for any project, always double-check your measurements and formulas to ensure you get an accurate estimation, especially for large structures, as it can save you time and resources in the long run.

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