Length of square =2r
Area of square =(2r)2=(2×7)2=142=196 cm2
Area of Circle =πr2=722×72=722×7×7=22×7=154 cm2 196−154=42 cm2
(square, circle, area, radius, difference)
Get the complete, step-by-step math solution for: "Length of square = 2r Area of square = (2r)² = (2 × 7)² = 14² = 196 cm² Area of Circle = π r² = (22)/(7) × 7² = (22 × 7 × 7)/(7) = 22 × 7 = 154 cm² 19...". 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. Since the radius r is given as 7 cm, the diameter is 2×7=14 cm. Therefore, the side of the square is 14 cm.
Step 2: Calculate the area of the square
The area of a square is calculated by squaring the length of its side. With the side length determined as 14 cm, we can now calculate the area of the square.
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=7 cm, and using π=722, we can find the area of the circle.
Step 4: Calculate the area of the shaded region
The shaded region represents the area of the square that is not covered by the inscribed circle. To find this area, we subtract the area of the circle from the area of the square.