Let's assume the radius and height of the cylinder (and the cone carved out of it) is "r" and "h" respectively.
The volume of a cone is given by the formula V_cone = (1/3) * π * r^2 * h.
The volume of a cylinder is given by the formula V_cylinder = π * r^2 * h.
Since the cone is carved out of the cylinder, the remaining volume is given by the formula V_remaining = V_cylinder - V_cone.
Substituting the values, we get V_remaining = π * r^2 * h - (1/3) * π * r^2 * h.
Simplifying further, we get V_remaining = (2/3) * π * r^2 * h.
Given that the volume remaining is 144 in^3, we can equate the equation to 144: (2/3) * π * r^2 * h = 144.
To find the volume of the original cylinder, we need to calculate V_cylinder which is given by the formula V_cylinder = V_cone + V_remaining.
Substituting the values, we get V_cylinder = V_cone + (2/3) * π * r^2 * h.
Since the cone and cylinder share the same radius and height, we can further simplify it as V_cylinder = V_cone + (2/3) * V_cone.
Substituting the formula for V_cone, we get V_cylinder = (1/3) * π * r^2 * h + (2/3) * (1/3) * π * r^2 * h.
Simplifying further, we get V_cylinder = (1/3 + 2/9) * π * r^2 * h.
Calculating the common denominator, we get V_cylinder = (3/9 + 2/9) * π * r^2 * h.
Simplifying further, we get V_cylinder = (5/9) * π * r^2 * h.
Now, we have the volume of the original cylinder in terms of the given variables.
A sculpture is a design by carving a cone out of a cylinder. The cone and cylinder share the same radius and height. If the volume remaining is 144 in^3. What was the volume of the original cylinder
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