FTCE General Knowledge Math Practice Test

What is the formula for the volume of a cylinder?

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

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

3. (3.14)(r)(h)

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

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

The volume of a cylinder is determined by the formula that incorporates the area of its base and its height. For a cylinder, the base is a circle, and the area of a circle is calculated using the formula \( \pi r^2 \), where \( r \) is the radius of the circle. To find the volume of the cylinder, this area is multiplied by the height \( h \) of the cylinder. Therefore, the correct formula for the volume of a cylinder is: \[ V = \pi r^2 h \] In this case, when using \( 3.14 \) as an approximation for \( \pi \), the formula becomes \( (3.14)(r^2)(h) \). This is why the answer is correct. The other choices reflect different calculations or concepts unrelated to the volume of a cylinder. One option describes the surface area of a cylinder, which includes both the lateral area and the areas of the two circular bases. Another option incorrectly states the volume as a linear term, while yet another option represents the formula for the volume of a sphere. This differentiation in formulas illustrates the importance of understanding the geometric properties associated with various three-dimensional shapes.