What is the surface area of the cube formed by a pattern of 4 squares in a row, each with a side length of 3 cm, and an additional square on both the top and bottom of the fourth s... What is the surface area of the cube formed by a pattern of 4 squares in a row, each with a side length of 3 cm, and an additional square on both the top and bottom of the fourth square?
Understand the Problem
The question describes a net (or pattern) that can be folded to form a cube. It asks us to calculate the surface area of the cube. First, we need to determine how many faces the described pattern has, then use the side length of the squares to calculate the area of each face, and finally calculate the total surface area of the cube.
Answer
$150 \text{ cm}^2$ ```
Answer for screen readers
$150 \text{ cm}^2$
Steps to Solve
- Identify the number of faces in the net
By examining the description, we can infer that the net is made up of 6 squares. This is because a cube has 6 faces.
- Determine the area of one face
Each face is a square with a side length of 5 cm. The area of a square is side $\times$ side. Therefore, the area of one face is $5 \text{ cm} \times 5 \text{ cm} = 25 \text{ cm}^2$.
- Calculate the total surface area of the cube
Since a cube has 6 faces, the total surface area is the area of one face multiplied by 6. $$ \text{Total Surface Area} = 6 \times 25 \text{ cm}^2 = 150 \text{ cm}^2 $$
$150 \text{ cm}^2$
More Information
A cube is a special type of cuboid where all sides are equal. It is also one of the five platonic solids.
Tips
A common mistake is to calculate the perimeter of a square instead of the area, or to incorrectly calculate the area of a square. Another mistake might be forgetting that a cube has 6 faces.
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