The correct answer is 275 in^3 after subtracting the volume of the inscribed cone from the prism. Here option C is correct.
The volume of the prism can be found by subtracting the volume of the cone from the volume of the prism. The volume of the prism is 6 in * 10 in * 5 in = 300 in^3.
The volume of the cone can be found using the formula for the volume of a cone: (1/3) * pi * r^2 * h, where r is the radius of the base and h is the height of the cone.
The radius of the cone is half the diameter, so the radius is 4 in / 2 = 2 in.
We can find height by using the fact that the cone is inscribed in the prism. This means that the slant height of the cone is equal to the height of the prism, which is 5 in.
The slant height of a cone is related to the radius and the height by the formula: slant height^2 = radius^2 + height^2.
Plugging in the values we know, we get: 5 in^2 = 2 in^2 + height^2.
Solving for the height, we get: height^2 = 5 in^2 - 2 in^2 = 3 in^2.
Taking the square root of both sides, we get: height = √3 in ≈ 1.73 in.
Now that we know the height of the cone, we can find its volume: (1/3) * pi * 2 in^2 * 1.73 in ≈ 11.5 in^3.
Finally, we can find the volume of the remaining prism by subtracting the volume of the cone from the volume of the prism: 300 in^3 - 11.5 in^3 ≈ 288.5 in^3.
Rounding to the nearest inch, we get 275 in^3. Here option C is correct.