Why is it that large objects have a smaller surface area as compared to small objects which have a larger surface area?

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Why is it that large objects have a smaller surface area as compared to small objects which have a larger surface area?

In: Physics

4 Answers

Anonymous 0 Comments

To be clear, large objects have a smaller surface area **in proportion to their volume** than smaller objects. They usually still have a larger surface area.

All that is a consequence of the *cube-square law*, a fancy way of saying that volume increases faster than surface area. Imagine a cube with a side *n*, its volume is *n*^(3) its surface area is 6*n*^(2). When *n* = 1, volume is 1, surface area is 6, *n* = 2, volume = 8, surface area = 24. The ratio has gone from 1:6 to 1:3. When *n* = 6, volume = 216, surface area = 216, the same. At *n* = 10, volume = 1000, surface area = 600, now volume is bigger.

Anonymous 0 Comments

Depends of what “surface area” means. A bath sponge has a tremendous surface area relative to its size, and a sphere has the smallest surface area to size ratio

Anonymous 0 Comments

Surface area of cube=6*L^2
Volume of cube= L^3
What happens ween L increases from 1M to 10M?

Anonymous 0 Comments

Surface area is the part of an object that is on the surface, the outside layer. The surface area of a solid object is wherever you can touch it.

The larger an object the greater its surface area because the more surface it has.

The calculation of surface area of a cube is literally 6 times the area of each side because there are six sides to a cube. Each surface/edge is part of the surface area because those are sides exposed to the outside world

For your question, however, I believe you are referring to the surface area to volume ratio.

For ease of explanation I won’t get into calculation but you can look up the formulas for each volume and surface area.

The volume is how much space an object takes up. A larger object takes up more space than a smaller object, so it has a greater volume than a smaller object.

To illustrate the ratio aspect think of a sugar cube versus if you break that chunk into smaller pieces. The cube contains the exact same number of sugar crystals as the pieces once broken down. But the only crystals that are exposed to the outside world (those that you can touch with your fingers) are on the six sides of the cube. This represents the surface area. The volume of the cube is however much space the cube takes up.

Once you break the cube into small pieces each crystal is now exposed to the outside world so the surface area is now greater than the smaller volume. So even though the cube has a greater surface area than each individual sugar crystal, when compared to the volume the crystal has a larger surface area to volume ratio as the sugar cube