Which equation correctly provides the volume of a cylinder?

Which equation correctly provides the volume of a cylinder?

• A. V = πr²h
• B. V = B + h
• C. V = 2Bh
• D. V = lwh

Answer: (A)

The equation that correctly represents the volume of a cylinder is V = πr²h. In this formula: - The variable \( V \) stands for volume. - The variable \( r \) represents the radius of the circular base of the cylinder. - The variable \( h \) denotes the height of the cylinder. - The term \( πr² \) calculates the area of the circular base of the cylinder. To find the volume, you multiply the area of the base by the height, which captures how much three-dimensional space the cylinder occupies. This geometric relationship is fundamental to understanding volumes in both mathematical and practical applications. Other options do not apply specifically to the formula for a cylinder. For example, B simply adds the area of a base and height but does not appropriately measure volume. C indicates a volume formula that suggests the use of two different areas multiplied by height; however, it does not reference any dimensional qualities unique to a cylinder. Lastly, D describes the volume of a rectangular prism, which is fundamentally different from the cylindrical shape and its volume calculation. Thus, the selection of V = πr²h is the only correct equation for determining the volume of a cylinder.

The equation that correctly represents the volume of a cylinder is V = πr²h. In this formula:

• The variable ( V ) stands for volume.

• The variable ( r ) represents the radius of the circular base of the cylinder.

• The variable ( h ) denotes the height of the cylinder.

• The term ( πr² ) calculates the area of the circular base of the cylinder.

To find the volume, you multiply the area of the base by the height, which captures how much three-dimensional space the cylinder occupies. This geometric relationship is fundamental to understanding volumes in both mathematical and practical applications.

Other options do not apply specifically to the formula for a cylinder. For example, B simply adds the area of a base and height but does not appropriately measure volume. C indicates a volume formula that suggests the use of two different areas multiplied by height; however, it does not reference any dimensional qualities unique to a cylinder. Lastly, D describes the volume of a rectangular prism, which is fundamentally different from the cylindrical shape and its volume calculation. Thus, the selection of V = πr²h is the only correct equation for determining the volume of a cylinder.