What is the formula for finding the volume of a cylinder?

• A. V = πr²h
• B. V = 2πrh
• C. V = πr²
• D. V = lwh

Answer: (A)

The formula for finding the volume of a cylinder is given by V = πr²h. In this formula, "V" represents the volume, "r" is the radius of the circular base of the cylinder, and "h" is the height of the cylinder. The reason this formula is derived in this manner is that the volume of any three-dimensional shape can often be calculated by determining the area of its base and then multiplying that area by its height.

For a cylinder, the base is a circle. The area of a circle is calculated using the formula A = πr². Once we have the area of the base, we then extend that area vertically by the height "h" of the cylinder. Therefore, the complete formula becomes Volume = Area of the base × Height = πr² × h.

This understanding is critical when visualizing how the volume is determined. It incorporates both the characteristics of the circular base and the height, effectively combining them to illustrate the amount of space the cylinder occupies.