The image depicts a mathematical problem where one must calculate the area of an inscribed circle within a square measuring 16cm per side. By determining that its radius is half its diameter (8cm), applying A=πr^2 yields an area of 64π cm^2.
The image presents a mathematical problem involving geometry, specifically focusing on the calculation of the area of a circle enclosed within a square. The diagram illustrates a circle with an unspecified radius, inscribed in a square with sides measuring 16 cm each. To determine the area of the circle, one must first ascertain its radius.
The diameter of the circle is equal to the side length of the square, given that it is inscribed within it. Consequently, with a 16 cm side length for the square, we deduce that the diameter of the circle is also 16 cm. Dividing this by two gives us an 8 cm radius for the circle.
With this information at hand, we can apply the formula for calculating the area of a circle: A = πr^2 (where ‘A’ represents area and ‘r’ denotes radius). Substituting our obtained values into this equation yields A = π(8)^2 = 64π cm^2.
This geometric configuration exemplifies how different shapes can relate to each other in terms of dimensions and areas. It underscores fundamental principles in geometry that are applicable in various real-world contexts including architecture, engineering, and design where understanding relationships between different geometrical shapes is pivotal.
In essence, this problem serves as an educational tool aimed at enhancing learners’ comprehension of geometric principles and their applications. It fosters analytical thinking and problem-solving skills by requiring students to apply knowledge in geometry to derive solutions logically.