The volume of a cone is given by the formula:
Volume cone = 1/3 * π * r^2 * h,
where r is the radius and h is the height of the cone.
The volume of a cylinder is given by the formula:
Volume cylinder = π * r^2 * h.
Since the cone and cylinder have the same radius and height, we can calculate the volume of the cone that was removed by subtracting the volume of the cone from the volume of the cylinder.
Volume cone = 1/3 * π * r^2 * h = 1/3 * π * (54 in^3) = 18π in^3.
Volume remaining = Volume cylinder - Volume cone = 54 in^3 - 18π in^3 ≈ 54 in^3 - 18 * 3.14159 in^3 ≈ 54 in^3 - 56.54866 in^3 ≈ -2.54866 in^3.
The volume remaining cannot be negative, so we discard this result.
Therefore, the correct answer is not provided among the options given.
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 54 in^3, what is the volume of the amount remaining?
A 40 inches^3
B 27 inches^3
C 36 inches^3
D 18 inches^3
3 answers
If we had to pick one, which is the closest?
The closest option to the calculated result of -2.54866 in^3 would be D) 18 inches^3, but note that this is not the exact answer.
1 answer