Jeffrey is buying dirt for a circular flower garden with a diameter of 12 feet. The layer of dirt needs to be 4 inches thick. What is the volume of dirt needed for the flower garden?
First, we need to convert the thickness of the layer of dirt from inches to feet. There are 12 inches in a foot, so 4 inches is equal to 4/12 = 1/3 feet.
The radius of the circular flower garden is half of the diameter, so the radius is 12/2 = 6 feet.
The volume of the dirt needed for the flower garden can be calculated using the formula for the volume of a cylinder, which is V = πr^2h, where V is the volume, π is a constant (approximately 3.14159), r is the radius, and h is the height or thickness.
Substituting in the values we know, the volume is V = 3.14159 * 6^2 * 1/3 = 3.14159 * 36 * 1/3 = 37.699.
Therefore, the volume of dirt needed for the flower garden is approximately 37.699 cubic feet.