What is the surface area of the cube formed by the pattern below, where the pattern is a net of a cube formed by a row of 4 squares each of side length 3 cm with a square on the to... What is the surface area of the cube formed by the pattern below, where the pattern is a net of a cube formed by a row of 4 squares each of side length 3 cm with a square on the top and the bottom of the fourth square?
Understand the Problem
The question asks to find the surface area of a cube formed by a given net (pattern). The net consists of a row of four squares, with one square attached to the top and another to the bottom of the last square in the row. Each square has a side length of 3 cm. To solve this, we need to recognize that this net can indeed form a cube, count the number of squares that make up the cube's surface, and then calculate the total surface area using the side length of each square.
Answer
$54 \text{ cm}^2$
Answer for screen readers
$54 \text{ cm}^2$
Steps to Solve
- Identify the shape formed by the net
The given net, consisting of six squares connected in a specific way, will form a cube when folded.
- Determine the number of faces of a cube
A cube has 6 faces, and each face is a square.
- Calculate the area of one square face
The area of one square face is given by the formula: Area = side * side. Since each side is 3 cm, the area of one face is $3 \text{ cm} \times 3 \text{ cm} = 9 \text{ cm}^2$.
- Calculate the total surface area of the cube
Since the cube has 6 faces, and each face has an area of $9 \text{ cm}^2$, the total surface area is $6 \times 9 \text{ cm}^2 = 54 \text{ cm}^2$.
$54 \text{ cm}^2$
More Information
A cube is a three-dimensional solid object bounded by six square faces, facets or sides, with three meeting at each vertex. It is one of the five Platonic solids. The cube is also a square parallelepiped, an equilateral cuboid and a right rhombohedron. It is a regular hexahedron. It is a special type of square prism and is also a zonohedron.
Tips
A common mistake would be to only calculate the area of one square and forget to multiply by the total number of faces, which is 6. Also, mistakes can be made in the multiplication of $6 \times 9$.
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