Final answer:
The electron-dense material surrounding the centrioles within the centrosome is known as the pericentriolar material. It is a key structure in organizing microtubules in the cell.
Step-by-step explanation:
The amorphous, electron-dense material that surrounds the two barrel-shaped centrioles and is part of the centrosome is known as the pericentriolar material. The centrosome acts as the main microtubule-organizing center in animal cells and is critical for the proper formation of the spindle apparatus during cell division. Each centrosome contains a pair of centrioles, with each centriole being a cylinder composed of nine triplets of microtubules, held together by nontubulin or other proteins. These proteins form a matrix around the centrioles, crucial for anchoring and nucleating microtubules, performing various roles in cell function, especially during mitosis.