FTCE Professional Education Practice Exam

Which calculation provides the volume of a right cone?

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

2. 4/3(3.14)(r^3)

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

4. 1/2PI

The correct answer is: 3.14(r^2)(h)/3

To determine the volume of a right cone, the correct formula is derived from the geometric principles of cones. A cone can be thought of as a pyramid with a circular base, and its volume is calculated using the formula V = (1/3) × base area × height. In the case of a right cone, the base is a circle, and the area of a circle is given by A = πr², where r represents the radius of the circle. To find the volume of the cone, you multiply the area of the base by the height (h) of the cone and then multiply that result by 1/3, which gives us the formula: Volume = (1/3) × πr² × h. When π is approximated as 3.14, this becomes: Volume = (3.14 × r² × h) / 3. This clearly shows why the first option represents the correct formula for calculating the volume of a right cone. The other choices either represent different geometric shapes entirely or do not apply to the volume calculation for a right cone specifically.