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First, we need to calculate the radius of the cylinder, which is half of the diameter. So, radius = 15 feet / 2 = 7.5 feet.
Next, we can calculate the volume of the cylinder using the formula V = πr^2h, where r is the radius and h is the height.
V = 3.14 x (7.5 feet)^2 x 40 feet
V = 3.14 x 56.25 square feet x 40 feet
V = 3.14 x 2250 cubic feet
V = 7065 cubic feet
Therefore, the volume of corn that the farmer can store in the silo is 7065 cubic feet.