Final answer:
After calculating the area of the circle (576π cm²) and the square (1681 cm²), it is evident that the circle has a greater area. The correct answer is a) The circle has the greatest area, by 355π cm².
Step-by-step explanation:
To determine which has the greater area, the circle or the square, we start by calculating the area of each shape using their respective formulas. For a circle, the area = πr², where r is the radius. For a square, the area = side length squared.
First, the circle has a diameter of 48 cm, so its radius r is half of that, which is 24 cm. The area of the circle is A = π(24 cm)² = 576π cm².
Next, the square has a side length of 41 cm, so its area A = (41 cm) x (41 cm) = 1681 cm².
Comparing these areas, the circle's area is 576π cm² and the square's area is 1681 cm². To make a direct comparison, we need to approximate π, which is about 3.1416. Therefore, the circle's area in decimal form is approximately 1809.56 cm².
Even without exact calculations, we can see that the square has a greater area than the circle, since 1681 cm² (the square) is less than 1809.56 cm² (the circle), and therefore answer a) is correct: The circle has the greatest area, by 355π cm².