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The smallest surface area for a given volume is a sphere. A spherical object such as a balloon represents the minimum energy required to maintain the volume of the material within. A balloon filled with water if stretched will increase the surface area of the balloon without altering the volume as water is non-compressible. Any alternative shape that encloses the same volume will have a larger surface area than a sphere.

A perfect example is a drop of liquid in a zero gravity environment which will vibrate when intially created but will gradually slow to a stop and take the form of a perfect sphere.

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14y ago
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5mo ago

You can increase the surface area of an object by changing its shape to include more edges or faces. For example, flattening or elongating the object can increase the surface area without increasing the volume.

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Q: How do you increase the surface area withour increasing the volume?
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What happens to the volume and surface area of a cell as a cell becomes larger?

They both increase with increasing cell radius (if we model a cell as a sphere). However, the rate of increase of the surface area is in general slower (dA/dr = 8πr) compared to the rate of increase of the volume (dV/dr = 4πr2). This would mean that with increasing cell size, the surface area to volume ratio is becoming smaller and smaller, giving a cell less surface area for the transport of nutrients for a given unit volume.


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The surface-to-volume ratio is a mathematical relationship between the volume of an object and the amount of surface area it has. This ratio often plays an important role in biological structures. An increase in the radius will increase the surface area by a power of two, but increase the volume by a power of three.


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