Assume that all linear dimensions of an animal increase by 12%. Then the animal will have the same shape. How do the surface area, the volume and the weight (under assumption of constant specific gravity) increase? Give the percentage of the increase.
To determine how the surface area, volume, and weight of an animal increase when all linear dimensions increase by 12%, we need to use the concept of scaling relationships.
1. Surface Area:
The surface area of an object is proportional to the square of its linear dimensions. In this case, if all linear dimensions increase by 12%, the new surface area would increase by (1.12)^2 = 1.2544 or approximately 25.44%.
2. Volume:
The volume of an object is proportional to the cube of its linear dimensions. Therefore, if all linear dimensions increase by 12%, the new volume would increase by (1.12)^3 = 1.4049 or approximately 40.49%.
3. Weight:
Under the assumption of constant specific gravity (density), the weight of an object is directly proportional to its volume. So, if the volume increases by 40.49% as mentioned earlier, the weight of the animal would increase by the same percentage, also around 40.49%.
In summary, if all linear dimensions of an animal increase by 12%, the surface area would increase by approximately 25.44%, the volume would increase by around 40.49%, and the weight (assuming constant specific gravity) would also increase by approximately 40.49%.