How Wide Should a Cement Support Pillar Be to Meet Weight Requirement?

Question:

If the plan is to pour a cylindrical pillar 10 feet tall, how wide should the pillar be?

Given:

Height = 10 feet

Portland cement density = 94 pounds per cubic foot

Weight requirement = 800 pounds

Calculation formula: [tex]V = \\pi r^2h[/tex]

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Answer:

The pillar should have a width of at least 2.134 feet to meet the weight requirement.

To comply with local regulations, a cement support pillar must contain at least 800 pounds of cement. In this case, if the plan is to pour a cylindrical pillar that is 10 feet tall, we need to determine the required width of the pillar to meet the weight requirement.

First, we need to calculate the volume of the pillar using the formula for the volume of a cylinder: [tex]V = \\pi r^2h[/tex], where V is the volume, r is the radius, and h is the height.

Given that the height of the pillar is 10 feet and the weight requirement is 800 pounds, we can set up the inequality: [tex]\\pi x^2 * 10\\geq 800 / 94[/tex], where x represents the radius of the pillar.

Solving the inequality leads to the conclusion that the pillar should have a width of at least 2.134 feet to meet the weight requirement of 800 pounds. This calculation takes into account the density of Portland cement, which is 94 pounds per cubic foot.