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To find the volume of the container, we need to use the formula for the volume of a cylinder, which is V = πr^2h, where r is the radius and h is the height.
The diameter of the container is 13 centimeters, so the radius is half of that, which is 13/2 = 6.5 centimeters.
The height of the container is 24 centimeters.
Now we can calculate the volume using the formula:
V = π(6.5^2)(24)
V ≈ 3.14159(42.25)(24)
V ≈ 3.14159(1014)
V ≈ 3184.59926
Rounding to the nearest tenth of a cubic centimeter, the volume of the container is approximately 3184.6 cubic centimeters.
The correct answer is A, 3,185.6 cubic centimeters.