Final answer:
The question involves the formula for finding the volume of a cylinder, which is V = πr²h. The volume of a cylinder is calculated by the area of the circle at the base (πr²) times the height (h) of the cylinder. The student had an incorrect formula referencing a one-third factor which is used for cones, not cylinders.
Step-by-step explanation:
The student's question pertains to the formula for calculating the volume of a cylinder. The correct formula for the volume of a cylinder is not V = (1/3) * (π * r^2 * h), but rather V = πr²h. This formula states that the volume (V) of a cylinder can be found by multiplying the area of the base (which is a circle with radius r, thus πr²) by the height (h) of the cylinder.
For example, if you have a cylinder with a radius of 0.750 cm and a height of 5.25 cm, applying the formula would be as follows:
- Calculate the area of the base: A = πr² = 3.142 * (0.750 cm)² = 1.76625 cm²
- Calculate the volume: V = A * h = 1.76625 cm² * 5.25 cm = 9.2728125 cm³
If you encounter the volume formula V = πr²h in your studies and confuse it with the one-third factor that is used in the volume of a cone, remember that cylinders have parallel sides and their volume is simply the base area times height.