5. Information about three circles is listed below. . Circle \( P \) has a radius of 26 cm . . Circle \( Q \) has a diameter of 52 cm . Based on the informatius of 52 cm . A The area of Circle \( Q \) is larger than the area of Circle \( R \). B The area of Circle \( P \) is the smallest of all three circles. C The circumference of Circle \( Q \) is the same as Circle \( R \). D The circumference of Circle \( Q \) is the same as Circle \( P \).

To determine the accuracy of the statements regarding circles \( P \), \( Q \), and \( R \), let’s summarize what we know first. Circle \( P \) has a radius of 26 cm, which gives it an area of approximately 2,123.72 cm² (using the area formula \( A = \pi r^2 \)). Circle \( Q \) has a diameter of 52 cm, translating to a radius of 26 cm as well, and therefore, its area is identical to Circle \( P \), also around 2,123.72 cm². For Circle \( R \), without specific dimensions, we can’t directly evaluate it but we can deduce other relationships based on what's provided. So let's knock these statements out of the park: A: False – We can't compare Circle \( Q \)'s area to Circle \( R \) without knowing Circle \( R \)'s dimensions. B: False – The area of Circle \( P \) is equal to that of Circle \( Q \), not the smallest. C: Indeterminate – Without Circle \( R \)'s data, we cannot confirm equivalence in circumference. D: True – Since both Circle \( P \) and Circle \( Q \) share the same radius (26 cm), their circumferences must also be equal (Circumference = \( 2\pi r \)). Now, let's throw some fun facts into the mix! Did you know that the concept of a circle dates back thousands of years? Ancient civilizations like the Babylonians and Egyptians had a profound understanding of circles and used geometric principles in their architecture and astronomy. The circle is not just a shape; it's a symbol of eternity and wholeness, appearing in various cultures as a representation of the universe! As for real-world applications, circles are everywhere, from the wheels on your bike to the designs of clock faces or even sports fields! Engineers use circular shapes in designing buildings for stability and aesthetics, while artists might employ circular patterns to create captivating designs. Who knew geometry could be such a vital part of everyday life?