A sculptor created a design by carving a cone out of a cylinder. The cone and cylinder share the same radius and height. If the volume of the cylinder before removing the cone is 54in .^ 3 what is the volume of the amount remaining? (1 point) 18in .^ 3; 36in .^ 3; 40in .^ 3; 27in .^ 3
The volume of a cylinder is given by the formula V = π * r^2 * h, where r is the radius and h is the height.
Since the cone and cylinder have the same radius and height, the volume of the cone can be found by subtracting the volume of the cone from the volume of the cylinder.
The volume of the cone is given by the formula V = (1/3) * π * r^2 * h.
Let's call the volume of the cone V_cone, and the remaining volume V_remaining.
We know that V_cylinder = 54 in^3.
We want to find V_remaining, so we need to subtract V_cone from V_cylinder.
V_remaining = V_cylinder - V_cone
V_remaining = 54 in^3 - (1/3) * π * r^2 * h
We can simplify this expression by plugging in the values of the radius and height of the cylinder.
Since the radius and height of the cone and cylinder are the same, we can let r and h be the common values.
V_remaining = 54 in^3 - (1/3) * π * r^2 * h
Now, we can calculate the volume of the remaining amount by using π ≈ 3.14 and substituting the values of r and h.
V_remaining = 54 in^3 - (1/3) * 3.14 * r^2 * h
However, since we do not know the exact values of the radius and height, we cannot determine the exact value of the remaining volume.
Therefore, the answer cannot be determined with the given information.