A circle is inscribed in a square of side 8 cm. What is the area of the circle?

A circle is inscribed in a square of side 8 cm. What is the area of the circle? (2022)

A circle is inscribed in a square of side 8 cm. What is the area of the circle? (2022)

Step 1: Identify the side length of the square, which is given as 8 cm.
Step 2: Understand that the circle is inscribed in the square, meaning the circle touches all four sides of the square.
Step 3: Calculate the radius of the circle. Since the diameter of the circle is equal to the side length of the square, the radius is half of the side length: 8 cm / 2 = 4 cm.
Step 4: Use the formula for the area of a circle, which is Area = π * r².
Step 5: Substitute the radius into the formula: Area = π * (4 cm)².
Step 6: Calculate (4 cm)², which is 16 cm².
Step 7: Multiply by π to find the area: Area = π * 16 cm².
Step 8: Use the approximate value of π (3.14) to calculate the area: Area ≈ 3.14 * 16 cm² = 50.24 cm².

Geometry of Circles and Squares – Understanding the relationship between the dimensions of a square and the inscribed circle, specifically how to derive the radius and area of the circle.
Area Calculation – Applying the formula for the area of a circle (A = πr²) correctly after determining the radius.