To lay a 1/2' thick base for a circular footer with a diameter of 30 feet, approximately 13 cubic yards of concrete are needed.
To lay a 1/2' thick base for a circular footer with a diameter of 30 feet, we need to calculate the volume of concrete required. The formula for the volume of a cylinder is V = πr^2h, where V is the volume, π is a constant (approximately 3.14), r is the radius, and h is the height.
In this case, the radius is half of the diameter, so r = 30/2 = 15 feet. Considering the thickness of 1/2', the height of the cylinder will be 1/2' = 1/2 feet.
Substituting these values into the formula, V = 3.14 * 15^2 * 1/2 = 3.14 * 225 * 1/2 = 352.75 cubic feet. Now, we need to convert this volume to cubic yards.
Since 1 cubic yard is equal to 27 cubic feet, the volume in cubic yards is 352.75 / 27 ≈ 13.04 cubic yards.
Therefore, we need approximately 13 cubic yards of concrete to lay a 1/2' thick base for the circular footer with a diameter of 30 feet.