FTCE Professional Education Practice Exam

What is the formula to find the volume of a pyramid?

1. 1/3Bh

2. 2(3.14)r^2

3. (3.14)(r^2)(h)

4. 4/3(3.14)(r^3)

The correct answer is: 1/3Bh

The formula to find the volume of a pyramid is expressed as \( V = \frac{1}{3} Bh \), where \( B \) represents the area of the base of the pyramid, and \( h \) is the height from the base to the apex (the top point) of the pyramid. This formula is derived from the general principle that the volume of a pyramid is one-third the product of the base area and its height. This can be understood because, geometrically, a pyramid can be thought of as a shape that tapers from a flat base to a point, and as such, it occupies one-third the space of a prism that has the same base area and height as the pyramid. The other options provided correspond to different geometric shapes: one is for the volume of a cylinder, another for the volume of a cone, and the last one for the volume of a sphere. This differentiation is crucial as each shape requires its own distinct formula based on its properties. Therefore, the correct choice accurately captures the relationship between the base area and height for calculating the volume of a pyramid.