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)
O 18 mm.³
O 36 in
40 in ³
O 27 Im.³

Answer 1

The volume of the remaining amount is 36 in³.

To find the volume of the cone that was carved out of the cylinder, we first need to find the volume of the cylinder before the cone was removed.

Given that the volume of the cylinder is 54 in³, we can use the formula V = πr²h, where r is the radius and h is the height of the cylinder.

Using the formula, we have:

V = 3.142 × (r)² × h

Since the cone and cylinder have the same radius and height, the volume of the cone is equal to one-third of the volume of the cylinder.

The volume of the remaining amount is then found by subtracting the volume of the cone from the volume of the cylinder:

Volume of remaining amount = Volume of cylinder - Volume of cone

So, the volume of the remaining amount is 54 - (54/3) = 54 - 18 = 36 in³.