FTCE General Knowledge Math Practice Test

How is the volume of a right cone calculated?

1. (3.14)(r^2)(h)/3

2. (3.14)(r)(square root of r^2 + h^2) + 3.14(r^2)

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

4. (3.14)(h)(r)

The correct answer is: (3.14)(r)(square root of r^2 + h^2) + 3.14(r^2)

The correct formula for calculating the volume of a right cone is given by the equation that involves the base area and the height. The standard formula is \( \text{Volume} = \frac{1}{3} \pi r^2 h \). This captures the essential components of the cone's volume. In the choices provided, while the other formulas focus on various aspects of geometric solids, the one that correctly reflects the volume of a cone is similar to the first choice, where \( \pi \) is a representation for approximately 3.14, \( r \) is the radius of the cone's base, and \( h \) is the height. This particular configuration emphasizes multiplying the area of the circular base (\( \pi r^2 \)) by the height \( h \), and then dividing by 3, which is characteristic of conical volumes. The options outlining additional calculations or configurations, like adding terms involving square roots or using different constants, do not apply to the specific formula for a right cone's volume, which purely relies on the base area and height relationship.