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)

Answer 1

Subtract the volume of the cone (one third of the cylinder's volume) from the volume of the cylinder to find the remaining volume. The volume of the material left after carving is 36 in.³.

Step-by-step explanation:

The sculptor is working with a cylinder and a cone that have the same radius and height.

When the cone is carved out of the cylinder, we need to subtract the volume of the cone from the volume of the cylinder to find the remaining volume. The volume of the cylinder (V = πr²h) is given as 54 in.³.

The formula for the volume of the cone is ⅓ of the volume of a cylinder with the same radius and height, so the cone's volume is ⅓ * 54 in.³ = 18 in.³.

Therefore, the volume of the remaining material after the cone is removed is 54 in.³ - 18 in.³ = 36 in.³.