表面积计算器
以下详细说明暂以英文提供。
How the surface area of each solid adds up
Surface area is the total area of every face, measured in square units. A cube has six identical square faces, so 6a². A rectangular prism has three pairs of matching faces, giving 2(lw + lh + wh). A cylinder contributes two circular caps (2πr²) plus the label wrapped around it, which unrolls to a rectangle of width 2πr and height h. A sphere is one smooth face of 4πr², and a cone is its round base plus a sector that unrolls to πr·s, where s = √(r² + h²) is the slant height.
Why paint and wrapping care about surface area
Surface area predicts how much coating, foil, or fabric covers a solid, while volume predicts what it holds — the two can move in opposite directions. Splitting a solid into pieces increases surface area but not volume, which is why crushed ice melts faster than one big block of the same mass. When estimating paint or sealer, compute the surface and subtract openings such as windows, then check the coverage figure printed on the can.
常见问题
Does the cylinder result include both ends?
Yes — the total counts the two circular caps as well as the curved wall. If your cylinder is open, such as a pipe section or an open tank, subtract one or both caps (πr² each) from the total.
What is slant height, and how is it different from height?
The height of a cone runs from the tip straight down to the center of the base; the slant height runs down the outside surface. They form a right triangle with the radius, so slant height = √(r² + h²). The cone tab computes it for you from radius and height.