Rectangular Prism / Box Calculator
Surface area is the total area of all faces or surfaces of a 3D object. It determines how much material is needed to cover an object (wrapping paper, paint, fabric) and is important in engineering, packaging, and biology (cell surface-to-volume ratios).
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Tip: Surface area always increases as the square of linear dimensions, while volume increases as the cube. Doubling all dimensions of a box quadruples its surface area but octuples its volume.
- 1Cube: SA = 6s² (s = side length)
- 2Rectangular prism: SA = 2(lw + lh + wh)
- 3Sphere: SA = 4πr²
- 4Cylinder: SA = 2πr² + 2πrh (top + bottom + lateral)
- 5Cone: SA = πr² + πrl (base + lateral, l = slant height)
Sphere, radius 5 cm=SA = 314.16 cm²4π(5²) = 100π
Cylinder, r=3, h=10=SA = 244.35 cm²2π(9) + 2π(3)(10) = 18π + 60π = 78π
| Shape | Formula | Variables |
|---|---|---|
| Cube | 6s² | s = side |
| Rectangular prism | 2(lw+lh+wh) | l,w,h = dimensions |
| Sphere | 4πr² | r = radius |
| Cylinder | 2πr(r+h) | r = radius, h = height |
| Cone | πr(r+l) | l = slant height = √(r²+h²) |
| Triangle prism | 2A + Ph | A = triangle area, P = perimeter, h = length |
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Fun Fact
Cells must maintain a high surface-area-to-volume ratio for efficient nutrient/waste exchange. This is why cells are small — if a cell doubled in linear size, its volume would increase 8× while surface area only increases 4×. This physical constraint limits cell size.
References
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