Final answer:
The statement is false. Energy from the Sun's core is carried away by radiation until about 70% of the way to the surface, after which it is transported by convection.
Step-by-step explanation:
The statement that, in the inner part of the Sun just above the core, energy is carried away via convection is false. In the Sun's interior, energy is generated in the core due to nuclear fusion. The core extends about one-quarter of the way to the surface, and contains about one-third of the Sun's mass. In this innermost region, energy is transported primarily by radiation, where it involves the absorption and reemission of photons. This mode of energy transport continues until about 70% of the way from the center to the surface, a zone known as the radiative zone. Beyond the radiative zone, starting approximately at the 70% radius mark and extending to the outer layers, energy is chiefly carried away by convection, where hot gas rises and cooler gas descends, forming convection currents.