To find the volume of the cone, we first need to find its radius. Since the pyramid is contained within the cone such that the vertices of the base of the pyramid are touching the edge of the cone, the diagonal of the square base of the pyramid is equal to the diameter of the base of the cone. The diagonal of the square base of the pyramid is:
d = √(10^2 + 10^2) = √200 = 10√2 cm
Therefore, the diameter of the base of the cone is 10√2 cm, and the radius is 5√2 cm.
The volume of the cone can be calculated using the formula:
V = (1/3)πr^2h
where r is the radius of the base of the cone and h is the height of the cone.
Substituting the given values, we get:
V = (1/3)π(5√2)^2(20)
V = (1/3)π(50)(20)
V = (1/3)(1000π)
V = 1000/3 * π
Using 3.14 as the decimal approximation for π, we get:
V ≈ 1046.35 cubic centimeters
Therefore, the volume of the cone is approximately 1046.35 cubic centimeters. The answer is A.