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.
The volume increase.
it's the problem of surface area -to- volume ratio that mean there is no fitting between increasing of surface area and increasing of volume
The kinetic energy will increase
The surface area of the cerebral cortex is increased by its folding into gyri and sulci. This folding allows for more neurons to be packed into a smaller space, increasing the brain's processing power without significantly increasing its size.
Simple answer: yes. It's a common theme in all aspects of the universe: the most efficient structure is that which maximizes its SURFACE AREA: VOLUME ratio. Plants and trees do this by having hairs on their roots, greatly increasing their surface area while minimally increasing volume. Side note, that's how the human intestine works too: it's full of small hairs called villi, which increase the surface area:volume ratio, therefore absorbing nutrients more efficiently.
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.
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.
The volume increase.
it's the problem of surface area -to- volume ratio that mean there is no fitting between increasing of surface area and increasing of volume
The volume will increase
Magnets.
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.
Holding volume constant while increasing mass will increase density. density = mass / volume
At constant volume the pressure increase.
To increase the solubility of a solute:Increase the temperature.Crsuh the solute to powder so you have a larger surface area to volume ratio.Increase the stirring/mixing rate.
The pressure would increase due to the decrease in volume, as pressure and volume are inversely related according to Boyle's Law. The temperature increase to 260 would further increase the pressure according to Gay-Lussac's Law, since pressure and temperature are directly related.
The kinetic energy will increase