- **Given Information:**
Two cubes with an edge of 10 centimeters are joined end to end to form a cuboid.
- **Calculating the Surface Area of the Resulting Cuboid:**
To find the surface area of the resulting cuboid, we need to consider the individual faces of the cuboid.
- **Front and Back Faces:**
The front and back faces of the cuboid will have an area equal to the product of the length and width of the cuboid. Since the cubes are joined end to end, the length of the resulting cuboid will be the sum of the edges of the cubes (10 cm + 10 cm = 20 cm). The width of the resulting cuboid will be equal to the edge of one of the cubes (10 cm).
Therefore, the area of the front and back faces = length * width = 20 cm * 10 cm = 200 square centimeters.
- **Top and Bottom Faces:**
The top and bottom faces of the cuboid will also have an area equal to the product of the length and width of the cuboid. The length remains the same (20 cm) and the height of the cuboid will be equal to the edge of the cube (10 cm).
Therefore, the area of the top and bottom faces = length * height = 20 cm * 10 cm = 200 square centimeters.
- **Side Faces:**
The side faces of the cuboid will have an area equal to the product of the width and height of the cuboid. The width is 10 cm and the height is also 10 cm.
Therefore, the area of the side faces = width * height = 10 cm * 10 cm = 100 square centimeters.
- **Total Surface Area:**
To find the total surface area of the resulting cuboid, we sum up the areas of all the faces:
Total surface area = 2(front + back) + 2(top + bottom) + 2(side) = 2(200) + 2(200) + 2(100) = 400 + 400 + 200 = 1000 square centimeters.
Therefore, the surface area of the resulting cuboid formed by joining two cubes of edge 10 centimeters end to end is 1000 square centimeters.