Answer :
The Volume of the oblique cone is approximately 402.12 cubic inches.
The volume of an oblique cone, we can use the formula:
V = (1/3) * π * r^2 * h,
where V is the volume, π is a mathematical constant approximately equal to 3.14159, r is the radius of the base, and h is the height of the cone.
In this case, the height of the cone is given as 6 inches. However, the slant height is provided, and we need to find the radius in order to calculate the volume.
Using the given information, we can apply the Pythagorean theorem to find the radius:
r^2 = slant height^2 - height^2,
r^2 = 10^2 - 6^2,
r^2 = 100 - 36,
r^2 = 64,
r = √64,
r = 8.
Now that we have the radius, we can calculate the volume:
V = (1/3) * π * (8)^2 * 6,
V = (1/3) * π * 64 * 6,
V = (1/3) * π * 384,
V = (384/3) * π,
V = 128 * π.
To find the decimal equivalent of the volume, we can multiply 128 by the value of π:
V ≈ 128 * 3.14159,
V ≈ 402.12.
Therefore, the volume of the oblique cone is approximately 402.12 cubic inches.
Among the given answer choices, the closest option is (B) 402.1 in³.
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