What are the formulas for the volume and surface area of a right cylinder?

The volume and surface area formulas for a right cylinder are essential components of geometry that help in understanding three-dimensional shapes. The volume of a right cylinder is calculated using the formula ( \pi r^2 h ), where ( r ) is the radius of the base and ( h ) is the height of the cylinder. This formula captures the essence of volume as it computes the area of the circular base (( \pi r^2 )) and multiplies it by the height, effectively stacking the circular areas across the height of the cylinder.

For the surface area, which includes both the curved surface area and the areas of the two circular bases, the formula is ( 2\pi rh + 2\pi r^2 ). The term ( 2\pi rh ) represents the lateral surface area (the curved side of the cylinder), while ( 2\pi r^2 ) accounts for the top and bottom circular bases. Together, these formulas provide a complete understanding of the cylinder's geometry, allowing one to compute both its capacity and the amount of material needed to cover it.

This answer corresponds correctly to the geometry of right cylinders and demonstrates a comprehensive understanding of the formulas involved. Other options do not encompass