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 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
40 in.3
40 in. cubed
36 in.3
36 in. cubed
18 in.3
18 in. cubed
27 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. Since the cone and the cylinder have the same radius and height, their volumes are equal.
Given that the volume of the cylinder before removing the cone is 54 in^3, the volume of the remaining amount is also 54 in^3.
Therefore, the correct answer is 54 in^3.
but u have to choose one of the answers above.
Apologies for the oversight. In that case, the correct answer from the options provided would be:
36 in.3 (or 36 in. cubed)
To find the volume of the amount remaining after carving out the cone, we need to subtract the volume of the cone from the volume of the cylinder.
Looking at the image, we can see that the height of the cylinder and cone are the same, and the radius of the cylinder is equal to the radius of the cone.
The volume of a cylinder is given by the formula V_cylinder = πr^2h, where r is the radius and h is the height.
Since the cone and cylinder have the same height and radius, the volume of the cylinder is also equal to the volume of the cone.
So, the volume of the cylinder = 54 in.3
And the volume of the cone = 54 in.3
To find the volume of the amount remaining, we need to subtract the volume of the cone from the volume of the cylinder.
Volume remaining = Volume of cylinder - Volume of cone
= 54 in.3 - 54 in.3
= 0 in.3
Therefore, the volume of the amount remaining after carving out the cone is 0 in.3.