Question

which of the following sentences is true about the relationship between the volume formulas for a cone and a cylinder with the same base area and height as the cone?
the volume of the cylinder and the cone are equal.
the volume of the cone is six times that of the cylinder.
the volume of the cone is one - third that of the cylinder.
the volume of the cylinder is three times the volume of the cone.

Explanation:

Step1: Recall the volume formulas

The volume formula for a cylinder is \(V_{cylinder}=B\times h\) (where \(B\) is the base area and \(h\) is the height). The volume formula for a cone is \(V_{cone}=\frac{1}{3}B\times h\).

Step2: Compare the two volumes

If we let \(B\) (base area) and \(h\) (height) be the same for both the cone and the cylinder. Then \(V_{cone}=\frac{1}{3}V_{cylinder}\), which can also be written as \(V_{cylinder} = 3V_{cone}\).

Answer:

The volume of the cone is one - third that of the cylinder and the volume of the cylinder is three times the volume of the cone. So the correct options are “The volume of the cone is one - third that of the cylinder” and “The volume of the cylinder is three times the volume of the cone”.