as an organism increases in size without any change in shape, its surface area to volume ratio in an endotherm (increases, decreases, stays the same, or not available)

Thank you for the opportunity to help you with your question!

For any defined shape, the surface area to volume ratio (denoted SA:V) is inversely proportional to the object's size. So as the object gets larger, so long as it shape stays the same, its SA:V will decrease. This is because as the shape gets larger, the volume becomes a larger portion of its overall size. Therefore the answer to your question is "decreases".

If you want proof of this just calculate the SA:V of two cubes, one larger than the other. You should see that the larger cube has a smaller SA:V

Most cells and organisms change their shapes when increasing size. This is to increase their surface area, which can have several benefits, such as better aerodynamics and increased exposure to the environment.

Please let me know if you need any clarification. I'm always happy to answer your questions.