Answer:
The area of the shaded region is (540 - 65.25pi) in²
Explanation:
The remaining part of the question which is an image is attached below.
Explanation:
To determine the area of the shaded region, that will be the difference between the area of the rectangle and the sum of the areas of the three circles.
First, we will determine the area of the rectangle, which is given by
Area of rectangle = Length × Breadth
In the figure, Breadth = 18 in
and Length = 12 in + 9 in + 6 in + 3 in
∴ Length = 30 in
Hence,
Area of rectangle = 30 in × 18 in
Area of rectangle = 540 in²
Now, we will determine the areas of the circles one after the other
For the smallest circle
From the figure, the diameter of the smallest circle is 6 in
From Radius = Diameter / 2
Hence,
Radius of the smallest circle = 6 in / 2 = 3 in
Area of a circle is given by
Area of circle = πr²
∴ For the smallest circle
Area of the smallest circle = π×3² = 9π in²
Hence, area of the smallest circle is 9pi in²
For the circle in the middle
Diameter of the circle in the middle is 9 in
∴ Radius of the circle in the middle = 9 in / 2 = 4.5 in
For the area of the circle in the middle
Area of the circle in the middle = π × 4.5² = 20.25π in²
Hence, Area of the circle in the middle is 20.25pi in²
For the largest circle
From the figure, the diameter of the largest circle is 12 in
Hence, radius of the largest circle = 12 in / 2 = 6 in
∴ For the largest circle
Area of the largest circle = π×6² = 36π in²
Hence, area of the largest circle is 36pi in²
Sum of the areas of the three circles = 9pi in² + 20.25pi in² + 36pi in²
Sum of the areas of the three circles = 65.25pi in²
Now,
Area of the shaded region = Area of the rectangle - Sum of the areas of the three circles
∴ Area of the shaded region = 540 in² - 65.25pi in²
Area of the shaded region = (540 - 65.25pi) in²
Hence, the area of the shaded region is (540 - 65.25pi) in²