To find the areas, we'll start with the circles and then calculate the area of the rectangle.
Areas of Both Circles
Given the radius of the first circle (r₁) is 4 cm: \[ A_1 = \pi r_1^2 = 3.14 \cdot (4^2) = 3.14 \cdot 16 = 50.24 , \text{cm}² \]
Given the radius of the second circle (r₂) is 9 cm: \[ A_2 = \pi r_2^2 = 3.14 \cdot (9^2) = 3.14 \cdot 81 = 254.34 , \text{cm}² \]
Now we can find the total area of both circles: \[ \text{Total Area of both circles} = A_1 + A_2 = 50.24 , \text{cm}² + 254.34 , \text{cm}² = 304.58 , \text{cm}² \]
Area of the Rectangle
The rectangle's dimensions are the diameters of the circles.
- Diameter of the first circle = 2 * 4 cm = 8 cm
- Diameter of the second circle = 2 * 9 cm = 18 cm
Let’s say the rectangle’s dimensions would be the same as the diameters of each circle, where the width is the larger diameter and the height is the smaller diameter.
The area of the rectangle is: \[ \text{Area of rectangle} = \text{Width} \times \text{Height} = 18 , \text{cm} \times 8 , \text{cm} = 144 , \text{cm}² \]
Total Surface Area (SA)
Now, to find the total surface area (comprised of both circles’ areas and the rectangle’s area): \[ \text{Total SA} = \text{Total Area of both circles} + \text{Area of rectangle} \] \[ \text{Total SA} = 304.58 , \text{cm}² + 144 , \text{cm}² = 448.58 , \text{cm}² \]
Summary of Results
- Both Circles: 304.58 cm²
- Rectangle: 144 cm²
- Total SA: 448.58 cm²