Date:
A circle of radius 6 cm is inscribed in a square. Find the area of the shaded region.
The image shows a square with side length 6 cm. Inside the square, there is an inscribed circle. The region between the square and the circle is shaded. The radius of the circle is 6 cm.
Get the complete, step-by-step math solution for: "Date: A circle of radius 6 cm is inscribed in a square. Find the area of the shaded region. The image shows a square with side length 6 cm. Inside the...". Powered by SolveForX AI math tutor.
Step-by-Step Solution
Step 1: Determine the side length of the square
When a circle is inscribed in a square, the diameter of the circle is equal to the side length of the square. Given that the radius of the circle is 6 cm, the diameter will be 2×6=12 cm. Therefore, the side length of the square is 12 cm.
Step 2: Calculate the area of the square
The area of a square is calculated by squaring its side length. Since the side length of the square is 12 cm, its area will be (12 cm)2=144 cm2.
Step 3: Calculate the area of the circle
The area of a circle is calculated using the formula πr2, where r is the radius. Given the radius r=6 cm, the area of the circle is π(6 cm)2=36π cm2.
Step 4: Calculate the area of the shaded region
The shaded region is the area of the square minus the area of the inscribed circle. Substituting the calculated areas, we get 144 cm2−36π cm2. This can also be written as 36(4−π) cm2.