Which of the following is true about the volume of a cylinder compared to a triangular pyramid with the same base area and height?

To understand why the volume of the triangular pyramid is half of the cylinder's volume, we can recall the formulas for the volume of each shape.

The volume ( V ) of a cylinder is calculated using the formula:

[

V = \text{Base Area} \times \text{Height}

]

For a triangular pyramid, the volume is given by:

[

V = \frac{1}{3} \times \text{Base Area} \times \text{Height}

]

When comparing the two shapes, both the cylinder and the triangular pyramid have the same base area and height. Therefore, if we substitute the base area and height into both formulas, we can clearly see their relationship.

If we take the volume of the cylinder as:

[

V_{\text{cylinder}} = \text{Base Area} \times \text{Height}

]

And the volume of the triangular pyramid as:

[

V_{\text{pyramid}} = \frac{1}{3} \times \text{Base Area} \times \text{Height}

]

It becomes apparent that the volume of the triangular pyramid is one-third that of the cylinder. This means that the volume of the pyramid is half