Carel van Schaik and Karin Isler explain:

Perhaps the most important limitation of brain size is the fact that brain tissue is metabolically very intensive and it, therefore, consumes a lot of energy. The heart, the liver and the kidneys need a similar amount of energy per gram of tissue. However, their size is much more determined by body weight than brain size i.e. it varies much less between species. Other organs, bones, muscles, skin etc. consume per gramme a fraction of the energy the brain consumes (…)

That means that it is more difficult to achieve a certain increase in brain size through natural selection than it is, for example, to achieve an equivalent increase in muscle mass or general body size.

Another difficulty is that an organism cannot temporarily shut down its brain to save energy because the brain needs exactly the same amount of energy at rest.
(Carel van Schaik, Karin Isler 2010: Gehirne, Le­bens­läufe und die Evolu­tion des Menschen, in: Fischer/ Wiegandt: Evolution, pp. 142-169, pp. 153s)

Since the brain is a very expensive organ, the considerable increase in brain size in the development into human beings through natural selection is an all the more astonishing process, one that requires a cogent explanation. Because one should actually expect that the energy-intensive human brain should not have survived evolution through the process of natural selection.

Accordingly, the history of evolutionary theory offers a wealth of solutions that are intended to explain the advantages of hominids having larger brains. My thoughts on the advantages of the growing brain for early humans will be presented in hypothesis 10.