To find the surface area of a square prism (also known as a rectangular prism when its base is a rectangle), we follow these steps. However, since the dimensions provided (3 cm, 3 cm, and 3 cm) indicate that it is a cube (which is a special case of a square prism), we will treat it as such.
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Identify the dimensions: All sides are 3 cm.
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Calculate the area of each face:
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Top and Bottom faces: Since the top and bottom are squares, the area of one square face is: \[ \text{Area of one square face} = \text{side}^2 = 3, \text{cm} \times 3, \text{cm} = 9, \text{cm}^2 \] There are 2 square faces (top and bottom): \[ \text{Total area for top and bottom} = 2 \times 9, \text{cm}^2 = 18, \text{cm}^2 \]
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Front and Back faces: Similar to the top and bottom, the front and back are also squares: \[ \text{Area of one square face} = 3, \text{cm} \times 3, \text{cm} = 9, \text{cm}^2 \] There are 2 square faces (front and back): \[ \text{Total area for front and back} = 2 \times 9, \text{cm}^2 = 18, \text{cm}^2 \]
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Side faces: The left and right sides are also squares: \[ \text{Area of one square face} = 3, \text{cm} \times 3, \text{cm} = 9, \text{cm}^2 \] There are 2 square faces (left and right): \[ \text{Total area for sides} = 2 \times 9, \text{cm}^2 = 18, \text{cm}^2 \]
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Total Surface Area: Now we add the areas of all the faces together: \[ \text{Total Surface Area (SA)} = \text{Top and Bottom} + \text{Front and Back} + \text{Sides} \] \[ \text{Total SA} = 18, \text{cm}^2 + 18, \text{cm}^2 + 18, \text{cm}^2 = 54, \text{cm}^2 \]
So the answers are:
- Top and bottom: 18 cm²
- Front and back: 18 cm²
- Sides: 18 cm²
- Total Surface Area: 54 cm²