Final answer:
The area of a circular logo increases by 300% when the diameter is enlarged to be 100% larger than the original, quadrupling the original area.
Step-by-step explanation:
When a circular logo's diameter is increased by 100%, it means the new diameter is twice as large as the original. Since the area of a circle is proportional to the square of its diameter, if you double the diameter, you quadruple (increase by a factor of four) the area.
The original area of the circle can be represented by πr2, where r is the radius. When the diameter is 100% larger, the new radius is twice the original radius. So the new area will be π(2r)2 = π4r2 = 4 × the original area.
Therefore, the area of the logo has increased by 300%, which is a threefold increase plus the original area.