What is the volume formula for a cylinder?

The formula for the volume of a cylinder is derived from its geometric properties. A cylinder is defined by its circular base and its height. To find the volume, you essentially calculate the area of the base and then multiply that area by the height of the cylinder.

The area of a circle is given by the formula πr², where r represents the radius of the circular base. The volume of the cylinder is then obtained by multiplying this area by the height (h) of the cylinder. This leads to the following formula:

Volume = Area of base × Height = πr² × h = πr²h.

This formula accurately represents the relationship between the radius, height, and total volume of a cylinder. Remember, the factors present in this formula depict how an increase in radius or height will proportionately increase the volume of the cylinder. The other formulas provided do not accurately account for both the area of the base and height in relation to the volume.