Use the image to answer the question. 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 18 in.3 18 in. cubed 36 in.3 36 in. cubed 27 in.3

We know that the volume of a cylinder is given by V = πr^2h, where r is the radius and h is the height.

Since the cone and cylinder share the same radius and height, we can calculate the volume of the cone as V_cone = (1/3)πr^2h.

The volume of the cylinder is given as 54 in^3, so we can set up the equation as:

54 = πr^2h

Solving for h, we find:

h = 54 / (πr^2)

Now, we can substitute the value of h into the volume formula of the cone to find the volume of the cone:

V_cone = (1/3)πr^2 * (54 / (πr^2))

V_cone = 54 / 3

V_cone = 18 in^3

Therefore, the volume of the remaining material after carving the cone out of the cylinder is given by:

Volume remaining = Volume of cylinder - Volume of cone
Volume remaining = 54 - 18
Volume remaining = 36 in^3

So the volume of the remaining material is 36 in^3.