A circle of radius 6 cm is inscribed in a square. Find the area of the shaded region. (π=722)
radius =6 cm
r=6; d=2×r=12 cm
Area of Square =d2=122=144 cm 2
Area of circle =πr2=722×6×6=7792
Area of shaded region =7144×7−792=71008−792=7216
Get the complete, step-by-step math solution for: "A circle of radius 6 cm is inscribed in a square. Find the area of the shaded region. (π = (22)/(7)) radius = 6 cm r = 6; d = 2 × r = 12 cm Area of Sq...". 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 the radius of the circle is 6 cm, we can find its diameter.
Step 2: Calculate the area of the square
Now that we have the side length of the square, we can calculate its area using the formula for the area of a square, which is side multiplied by side.
Step 3: Calculate the area of the circle
With the given radius and the value of π, we can calculate the area of the circle using the standard formula for the area of a circle.
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. We subtract the area of the circle from the area of the square to find the final answer.