Question

What is the relationship between the size of the organism and its surface area to volume ratio?

Answer 1

Hint: As the cell grows its volume also increases along with it. The surface-area-to-volume ratio is written as SA: V, where V is the sum of surface area per unit volume of an object or group of objects.

Complete answer:
When the cell grows, its volume also increases rapidly than its surface area. Surface area is the total area on the surface of an object. The formula for the surface area of a sphere is $4\pi {r^2}$. While the formula for its volume is $4\pi {r^3}/3$. Smaller single-celled organisms have a higher surface area than their volume ratio. Larger organisms need specialized organs for different functions of their body. When the volume increases it leads to many biological problems in them. And for smaller organisms with high surface area to volume ratio, they relatively have gravity much lesser than the large animals. However, the increased surface area can cause many problems. Animals lose heat in proportion to their surface area. The larger the surface area of the animals the amount of heat that loses from its body also increases. Animals generate heat internally in accordance with their volume. As the volume of the organisms increases the more it can produce heat. Let’s look at the relation between the size of the organism and its surface area to volume ratio mathematically. Let us consider two cubes of length, breadth, and height of\[1cm{\text{ }} \times {\text{ }}1cm{\text{ }} \times {\text{ }}1cm{\text{ }}and{\text{ }}3cm{\text{ }} \times {\text{ }}3cm{\text{ }} \times {\text{ }}3cm\]. We can see the first cube will have a SA: V of \[6:1\]and the second one will have\[2:1\]. Hence we can conclude that when the size of the organism increases lower is its SA: V ratio.

Note:
As the cells grow the surface to its volume ratio gets decreased. The smaller-sized organisms have a higher surface area than their volume. When we compare two cubes one smaller one and one bigger one, we can come to a conclusion that when the size of the organism increases lower is its SA: V ratio.