Given that the volume of the cylinder before removing the cone is 54 cm³, we can use the formula for the volume of a cylinder to find the radius and height of the cylinder.
The volume of a cylinder is given by the formula V = πr²h, where r is the radius and h is the height.
Since the volume of the cylinder is 54 cm³, we have:
54 = πr²h
Since the cone and cylinder share the same radius and height, the volume of the cone can be calculated using the formula V = (1/3)πr²h.
After removing the cone from the cylinder, the volume remaining is the volume of the cylinder minus the volume of the cone.
Therefore, the volume remaining is:
V_remaining = V_cylinder - V_cone
= πr²h - (1/3)πr²h
= (2/3)πr²h
= (2/3) * 54
= 36 cm³
Therefore, the volume of the amount remaining after removing the cone is 36 cm³.
Use the image to answer the question.
A cone is placed inside a cylinder. The apex of the cone touching the center of the top circle of the cylinder is highlighted with a dot. The cone with its base is drawn in dashed lines. The base of the cone is common with the base of the cylinder.
A cone is placed inside a cylinder. The apex of the cone touching the center of the top circle of the cylinder is highlighted with a dot. The cone with its base is drawn in dashed lines. The base of the cone is common with the base of the cylinder.
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 cm³, what is the volume of the amount remaining?
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