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?(1 point) Responses 18 in.3 18 in. cubed 27 in.3 27 in. cubed 36 in.3 36 in. cubed 40 in.3
The volume of a cylinder is given by the formula V = πr^2h, where r is the radius and h is the height.
In this case, since the cone and cylinder share the same radius and height, their volumes are the same.
The volume of the cone is given by the formula V = (1/3)πr^2h.
Since the volume of the cylinder before removing the cone is 54 in^3, the volume of the remaining amount will also be 54 in^3.
Therefore, the volume of the amount remaining is 54 in^3.
wrong
I apologize for the mistake.
To find the volume of the remaining amount, we need to subtract the volume of the cone from the volume of the cylinder.
Since the cone and cylinder share the same radius and height, the volume of the cone is given by (1/3)πr^2h and the volume of the cylinder is given by πr^2h.
The volume of the remaining amount is therefore:
Volume of cylinder - Volume of cone = πr^2h - (1/3)πr^2h = (2/3)πr^2h
Given that the volume of the cylinder before removing the cone is 54 in^3, we can set up the equation:
(2/3)πr^2h = 54
To solve for the remaining volume, we need to know the values for the radius and height of the cylinder, which are not provided in the question.
pick one of the answer 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?(1 point) Responses 18 in.3 18 in. cubed 27 in.3 27 in. cubed 36 in.3 36 in. cubed 40 in.3
To find the volume of the remaining amount, we need to subtract the volume of the cone from the volume of the cylinder. Since the cone and cylinder have the same radius and height, the volume of the cone will be one-third of the volume of the cylinder.
The volume of the remaining amount will be 2/3 of the volume of the cylinder.
Given that the volume of the cylinder before removing the cone is 54 in^3, we can calculate the volume of the remaining amount:
Volume of remaining amount = (2/3) * 54 in^3
= 36 in^3
Therefore, the volume of the amount remaining is 36 in^3.
To find the volume of the remaining material after removing the cone from the cylinder, we need to find the volume of the cone and subtract it from the volume of the cylinder.
The volume of a cylinder is given by the formula V_cylinder = 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 cylinder is 54 in^3. Therefore, we can set up the equation:
54 = π * r^2 * h
To find the volume of the cone, we use the formula V_cone = (1/3) * π * r^2 * h.
Substituting the value of r and h from the cylinder, we get:
V_cone = (1/3) * π * r^2 * h
Now, we can subtract the volume of the cone from the volume of the cylinder to find the remaining volume:
Remaining volume = V_cylinder - V_cone
Using the given values, we can now solve the equation to find the remaining volume.