What is the formula for the volume of a cylinder?

What is the formula for the volume of a cylinder?

• A. Volume = 2πr²h
• B. Volume = πr²h
• C. Volume = πd²h
• D. Volume = 2πrh

Answer: (B)

The volume of a cylinder is derived from its geometric properties. A cylinder consists of two circular bases and a height that connects these bases. To find the volume, you can start by calculating the area of the circular base, which is given by the formula \( \pi r^2 \), where \( r \) is the radius of the base. Once you have the area of the base, you multiply it by the height of the cylinder, denoted as \( h \). This results in the formula for the volume of a cylinder: \( \text{Volume} = \text{Base Area} \times \text{Height} = \pi r^2 h \). This is why the correct answer indicates that the volume is \( \pi r^2 h \). It precisely captures the relationship between the base area and the height of the cylinder, reflecting how much space is contained within the 3-dimensional shape based on its circular base and height.

The volume of a cylinder is derived from its geometric properties. A cylinder consists of two circular bases and a height that connects these bases. To find the volume, you can start by calculating the area of the circular base, which is given by the formula ( \pi r^2 ), where ( r ) is the radius of the base.

Once you have the area of the base, you multiply it by the height of the cylinder, denoted as ( h ). This results in the formula for the volume of a cylinder: ( \text{Volume} = \text{Base Area} \times \text{Height} = \pi r^2 h ).

This is why the correct answer indicates that the volume is ( \pi r^2 h ). It precisely captures the relationship between the base area and the height of the cylinder, reflecting how much space is contained within the 3-dimensional shape based on its circular base and height.