Examine the following graph.
Which of the following is correct?

• A. If the radius is doubled, the area also doubles.
• B. The area is inversely related to the radius.
• C. If the radius is 8, the area is 200 in².
• D. Based on the graph, Area = Radius².
• E. All of these statements are correct.

Answer: (C)

Verified step by step guidance

1. Examine the graph to understand the relationship between the radius and the area. Notice that the graph shows a curve, indicating a non-linear relationship.
2. Recall the formula for the area of a circle: \( A = \pi r^2 \), where \( A \) is the area and \( r \) is the radius. This suggests that the area is proportional to the square of the radius.
3. Check the statement 'If the radius is doubled, the area also doubles.' According to the formula \( A = \pi r^2 \), if the radius is doubled, the area becomes \( \pi (2r)^2 = 4\pi r^2 \), which means the area quadruples, not doubles.
4. Evaluate the statement 'The area is inversely related to the radius.' An inverse relationship would imply that as the radius increases, the area decreases, which is not supported by the graph or the formula \( A = \pi r^2 \).
5. Verify the statement 'If the radius is 8, the area is 200 in^2.' Locate the point on the graph where the radius is 8 inches and check the corresponding area value. This will help determine if this statement is correct.