What section of the human brain (containing the hemispheres and cortex) has more than 75% of its mass?

The cerebrum! The cerebrum is divided into two hemispheres and 4 main lobes. The frontal lobe is where our problem solving and memories are thought to occurs. The partial lobe is where sensory nerves like touch, pain, hot, and cold are processed. The Occupational lobe is where vision is processed. Finally the temporal lobe processes the other senses and things like language.

https://en.m.wikipedia.org/wiki/Human_brain

The four main lobes are:

Frontal lobe: The largest lobe of the brain, located in the front of the head, the frontal lobe is involved in personality characteristics, decision-making, and movement. Recognition of smell usually involves parts of the frontal lobe. The frontal lobe contains Broca's area, which is associated with speech ability.

Parietal lobe: The middle part of the brain, the parietal lobe helps a person identify objects and understand spatial relationships (where one's body is compared with objects around the person). The parietal lobe is also involved in interpreting pain and touch in the body. The parietal lobe houses Wernicke's area, which helps the brain understand spoken language.

Occipital lobe: The occipital lobe is the back part of the brain that is involved with vision.

Temporal lobe: The sides of the brain, temporal lobes are involved in short-term memory, speech, musical rhythm and some degree of smell recognition.

https://www.hopkinsmedicine.org/health/conditions-and-diseases/anatomy-of-the-brain