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.
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
1 answer
1 answer