FTCE Professional Education Practice Exam

How is the volume of a cylinder calculated?

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

2. 2(3.14)(rh) + 2(3.14)r^2

3. 3.14(r)(square root of r^2 + h^2)

4. 1/3Bh

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

The volume of a cylinder is calculated using the formula V = πr²h, where V represents volume, r is the radius of the base, and h is the height of the cylinder. The value of π (pi) is commonly approximated as 3.14, which leads to the equation (3.14)(r²)(h) for practical calculations. This formula works because the volume is derived from the area of the circular base (which is calculated as πr²) multiplied by the height (h) of the cylinder, effectively stacking the area of the base across the height of the cylinder. In the context of the other options, the second choice outlines the surface area of a cylinder rather than the volume, as it includes terms that calculate the areas of the two circular bases and the lateral surface area. The third choice appears to be a formula related to the slant height of a cone rather than a cylinder, which suggests a misunderstanding of the shape being evaluated. Lastly, the fourth choice represents the formula for the volume of a cone, specifically involving the base area (B) and height (h), which is distinctly different from the cylindrical volume calculation. Thus, the choice that correctly represents the volume of a cylinder