The volume of a cylinder is given by the formula $V=\pi r^2 h$, where $r$ is the radius of the cylinder and $h$ is the height. Which expression represents the volume of this cylinder?
Answer (2)
The volume of a cylinder is represented by the expression π r 2 h . This formula consists of the radius r and the height h of the cylinder. Therefore, the correct expression is π r 2 h .
;
The volume of a cylinder is given by the formula V = π r 2 h .
Identify the components: r is the radius and h is the height.
The expression representing the volume of the cylinder is π r 2 h .
Therefore, the volume of the cylinder is π r 2 h .
Explanation
Problem Analysis The problem states that the volume of a cylinder is given by the formula V = π r 2 h , where r is the radius of the cylinder and h is the height. We need to identify the expression that represents the volume of this cylinder.
Identifying the Expression The formula for the volume of a cylinder is directly given as V = π r 2 h . Therefore, the expression representing the volume is simply π r 2 h .
Final Answer The expression that represents the volume of the cylinder is π r 2 h .
Examples
Understanding the volume of a cylinder is crucial in many real-world applications. For example, when designing cylindrical storage tanks for liquids or gases, engineers use the formula V = π r 2 h to calculate the tank's capacity. Similarly, in architecture, calculating the volume of cylindrical columns helps determine the amount of material needed for construction. Even in everyday scenarios like baking, knowing the volume of a cylindrical cake pan helps in adjusting recipes and ensuring the cake fits perfectly. The formula is a fundamental tool in various fields for determining the space occupied by cylindrical objects.
