Is surface area ever equal to volume?
Two figures can have the same volume but different surface areas. For example: A rectangular prism with side lengths of 1 cm, 2 cm, and 2 cm has a volume of 4 cu cm and a surface area of 16 sq cm. A rectangular prism with side lengths of 1 cm, 1 cm, and 4 cm has the same volume but a surface area of 18 sq cm.
How do you convert surface area to volume?
For a cube, the equation for surface area is S=6*L*L, where L is the length of a side. Similarly, the volume of a cube is V =L*L*L. So for a cube, the ratio of surface area to volume is given by the ratio of these equations: S/V = 6/L.
How are surface and volume related?
As you can see from the formulas, surface area is square function (side 2 x 6), while volume is a cubic function (side)3. As a result, as the size of an object increases, its ratio of surface area to volume decreases. Conversely, as the size of an object decreases, its ratio of surface area to volume increases.
How does surface area to volume relate to how well a cell functions?
1: Surface Area to Volume Ratios: Notice that as a cell increases in size, its surface area-to-volume ratio decreases. When there is insufficient surface area to support a cell’s increasing volume, a cell will either divide or die.
How do you remember surface area and volume?
Surface Areas And Volumes
- To find the surface area of a solid, add the areas of all the faces. You can remember the formula as sum of areas of the all the faces.
- Volume of a prism is area of its base times height.
- Volume of a pyramid is one third of area of its base times height.
What is the surface area formula?
Variables:
| Surface Area Formula | Surface Area Meaning |
|---|---|
| SA=B+12sP | Find the area of each face. Add up all areas. |
| SA=2B+2πrh | Find the area of the base, times 2, then add the areas to the areas of the rectangle, which is the circumference times the height. |
| SA=4πr2 | Find the area of the great circle and multiply it by 4. |
How does volume increase compared to surface area?
As the radius of a cell increases, its surface area increases as the square of its radius, but its volume increases as the cube of its radius (much more rapidly). Therefore, as a cell increases in size, its surface area-to-volume ratio decreases.