Surface Area
Calculate surface area of 3D shapes
How to use Surface Area
- 1Select a three-dimensional shape (cube, ball, cylinder, cone, etc.).
- 2Enter its dimensions, such as radius, height or edge length.
- 3View the area of the matrix and give a separate side area, if necessary.
Calculate surface area
Cube =2 lw + lh + wh; ball = 4 πr2; cylinder = 2 πr (r + h)The surface area is the sum of all outer surfaces of a stereo in square units.
It relates to the materials needed to make, paint or package the object, which is measured in volume.
There is a pattern in the memory of the surface area formula: ** The surface area of the polyhedrus is the sum of the surface areas.** Cube 6 is the same square, so 6a2 is the same; the rectangular 3 is the same, so 2 (lw + lh + wh). A curved graphic needs to be understood. – The side of the cylinder is extended in a rectangle, with a width equal to 2 gills at the bottom perimeter, and above h, so the side area is 2 gills, plus 2 gills at the bottom two.
In the case of the Internet, it is easy to make mistakes in the application. Only four walls and ceilings (not including floors) will be required to paint the room, and only one side will be required to make iron for an uncovered water tank. Another common confusion is the cone's main line l and the high h - the main line is tilted, l = √ (r2 + h2) and the formula uses the main rather than the high line. Mixing makes the side size wrong.
| Shape | Table area | Volume | Parameter Description |
|---|---|---|---|
| Cube | 6a² | a³ | a = Prism |
| rectangular | 2(lw + lh + wh) | lwh | l/w/h = long/wide/high |
| Sphere | 4πr² | (4/3)πr³ | r = Radius |
| Cylinder | 2πr² + 2πrh | πr²h | r = bottom radius, h = high |
| Circle | πr² + πrl | (1/3)πr²h | l = carrier long |
Table size and volume formula for common stereo graphics
Frequently asked questions
Table size and volume?
Area is external (square units); volume is internal (cubic units).
What's the side area?
Side only, not top and bottom.
Why squared units?
The area is two-dimensional, so the unit takes the secondary side.
Why is the surface area of the ball exactly 4 gillr2?
There is a clever explanation: the surface area of the ball is exactly the size of its outer cut cylindrical column (theorem of the Akimid ball). The outer cylindrical base radius r, high 2r, side area = 2 πr x 2r = 4 πr2, equal to the surface area of the ball. Akimid was extremely proud of this discovery and demanded that the inside of the ball be carved on his gravestone. Another way to remember: the surface area of the ball is exactly four times the area of the same radius.
Which sizes of surface area and volume grow faster?
Faster volume - surface area increases by size square and volume increases by cube. This difference has important practical significance: when objects become larger, volume (by weight, heat) increases faster than surface area (by mass, weight area). This is why elephants have huge ears (increased heat area), why small-sized animals are more afraid of cold (relative surface area, high heat dispersion), and why large tablets are difficult to dissolve (relative surface area).