A prism has two times the volume of a pyramid with the same base and altitude.A.TrueB.False

Answer:

A. True

Explanation:

The volume of a pyramid is given by the formula:

$V_{\text{pyramid}} = \frac{1}{3} \cdot B \cdot h$

where $B$ is the area of the base and $h$ is the height.

The volume of a prism is given by the formula:

$V_{\text{prism}} = B \cdot h$

If we compare the volumes of a prism and a pyramid having the same base area and height, we can see that:

$V_{\text{prism}} = B \cdot h = 3 \cdot \left( \frac{1}{3} \cdot B \cdot h \right) = 3 \cdot V_{\text{pyramid}}$

This confirms that the volume of a prism is three times that of a pyramid with the same base and height.

Thus, since the statement says that the prism has two times the volume of the pyramid, it is false. The correct relationship is that the prism's volume is three times that of the pyramid.

Therefore, the correct answer is B. False.