The height of a cone is half the diameter of its base. If the cone’s height is 4 inches, what is the cone’s volume to the nearest cubic inch?

To find the volume of a cone, we need to know its height and the radius of its base. In this case, we are provided with the height of the cone. Let's calculate the radius of the cone's base first. The height of the cone is half the diameter of its base, which means the radius is half of the height.
Radius of the base = Height ÷ 2 = 4 ÷ 2 = 2 inches

Now, we can calculate the volume of the cone using the formula:
Volume = \( \frac{\mathrm{1} }{\mathrm{3}} \) × π × Radius^2 × Height = \( \frac{\mathrm{1} }{\mathrm{3}} \) × π × \(2^2\) × 4
Simplifying the expression:
Volume = \( \frac{\mathrm{1} }{\mathrm{3}} \) × 3.14 × 4 × 4 ≈ 67 cubic inches (rounded to the nearest whole number).

Therefore, the volume of the cone is approximately 67 cubic inches.