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

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

• A. V = 2πr²h
• B. V = πr²h
• C. V = πr² + h
• D. V = πdh

Answer: (B)

The formula for calculating the volume of a cylinder is given by V = πr²h. In this formula: - V represents the volume of the cylinder. - r is the radius of the circular base of the cylinder. - h is the height of the cylinder. - π (pi) is a mathematical constant approximately equal to 3.14159. To derive this formula, consider that a cylinder consists of a circular base and height extending perpendicular from the base. The area of the base, which is a circle, is calculated using the formula A = πr². Since the volume of a three-dimensional shape is found by multiplying the area of the base by its height, we extend this idea to cylinders by multiplying the area of the base (πr²) by the height (h). Therefore, the complete formula for the volume of a cylinder is V = base area × height = πr² × h. This relationship clearly shows how both the radius and height influence the overall volume of the cylinder, making B the correct choice. The other options incorporate incorrect mathematical relationships or aspects of geometry that do not apply to the volume of a cylinder, which is why they do not represent the correct formula.

The formula for calculating the volume of a cylinder is given by V = πr²h. In this formula:

• V represents the volume of the cylinder.

• r is the radius of the circular base of the cylinder.

• h is the height of the cylinder.

• π (pi) is a mathematical constant approximately equal to 3.14159.

To derive this formula, consider that a cylinder consists of a circular base and height extending perpendicular from the base. The area of the base, which is a circle, is calculated using the formula A = πr². Since the volume of a three-dimensional shape is found by multiplying the area of the base by its height, we extend this idea to cylinders by multiplying the area of the base (πr²) by the height (h).

Therefore, the complete formula for the volume of a cylinder is V = base area × height = πr² × h. This relationship clearly shows how both the radius and height influence the overall volume of the cylinder, making B the correct choice.

The other options incorporate incorrect mathematical relationships or aspects of geometry that do not apply to the volume of a cylinder, which is why they do not represent the correct formula.