To find the area of both circles and the surface area of the cylinder, we can follow these steps:
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Calculate the area of one base of the cylinder (circle) using the formula \( A = \pi r^2 \).
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Since the cylinder has two identical bases, we will multiply the area of one base by 2.
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Calculate the area of the rectangle (the side of the cylinder) using the formula for the lateral surface area of a cylinder \( SA_{rectangle} = 2\pi rh \).
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Combine the areas of the circles and the rectangle to find the total surface area.
Given:
- Radius (r) = 5 cm (assuming this is the radius of the base of the cylinder)
- Height (h) = 8 cm
Step 1: Area of one circle
\[ A = \pi r^2 = 3.14 \times (5)^2 = 3.14 \times 25 = 78.5 , \text{cm}^2 \]
Step 2: Area of both circles
\[ \text{Area of both circles} = 2 \times A = 2 \times 78.5 = 157 , \text{cm}^2 \]
Step 3: Area of the rectangle (lateral surface area)
\[ SA_{rectangle} = 2\pi rh = 2 \times 3.14 \times 5 \times 8 \] Calculating: \[ SA_{rectangle} = 2 \times 3.14 \times 5 \times 8 = 2 \times 3.14 \times 40 \] \[ SA_{rectangle} = 2 \times 125.6 = 251.2 , \text{cm}^2 \]
Step 4: Total surface area
\[ \text{Total SA} = \text{Area of both circles} + SA_{rectangle} = 157 + 251.2 = 408.2 , \text{cm}^2 \]
Summary of Answers
- Area of both circles: 157 cm²
- Area of rectangle: 251.2 cm²
- Total surface area: 408.2 cm²