# Surface area to volume ratio part I

The concept of surface are to volume ratio has an important bearing on many things, coffee and tea included. In this article I'll discuss what surface to volume ratio (SA/V) is, and for the next article, why it concerns coffee and tea. To understand SA/V we need to understand the components that make it up - area (more specifically surface area), and volume. Volume is simply how much space an object take up in a 3D world. The volume of a cube would be its length times its width times its height (since in the case of cube, the length, width, and height are equal, the volume can be represented as l³) The volume of an object can also be found by measuring the volume of water the object displaces when submerged. Again, volume is a 3D measurement and is commonly measured in Liters, gallons, fluid ounces, etc. Regardless of whether I fill a basketball with air or lead it would have the same volume.

Now on to area. Area is a 2D measurement of the space enclosed by a certain set of boundaries. The area of a square would be its length times its width (since in the case of square, the length and width are equal, the area can be represented as l²). Area is often measured in square meters, square feet, etc. Surface area is just the area of an object that is exposed to the environment; so it is still a 2D measurement, but it can be applied to 3D objects, like the surface area of a ball is 4?r² - while the volume of the ball is (4/3)?r³. The surface are to volume ratio of an object is just the surface area of the object divided by the volume of the object. So when calculating SA/V one is finding how much surface area the object has per the amount of volume the object takes up. So the higher the ratio, the more SA the object has per unit volume, thus the more direct contact the object has with its environment and will therefore react with the environment more rapidly. For example, a ping-pong ball would have a higher SA/V than a beach ball. Also, if I had a sheet of paper with the same volume as the ping-pong ball (which would be a huge piece of paper), the paper would have a higher SA/V. These can be inferred conceptually, or mathematically, depending on your preference.

Conceptually one can just think about which object has more SA per unit volume, and thus which one would react quicker with its environment. Mathematically, in the case of the ping pong and beach ball, you can see from the above equations that as the size of the ball increases (increasing radius) the SA will increase by the square of the radius while the volume will increase by the cube or the radius, therefore the volume will increase quicker because it is increasing at a cubic rate as opposed to the square rate of the SA. SA/V ratios and their effects are not easy concepts to fully grasp. Hopefully after reading this article and ruminating on it a bit you will have an understanding of the concept, and for next Mugg's Buzz I'll write about what all this stuff has to do with coffee and tea!