A (rectangular) cuboid is a closed box which comprises of 3 pairs of rectangular faces that are parallel to each other, and joined at right angles. It is also known as a right rectangular prism. It has 8 vertices, 6 faces, and 12 edges. The cube is a cuboid whose faces are all squares.
The figure above shows the developmental figure of a cuboid. Notice that the developmental figure consists of two faces, two faces, and two faces. The surface area of a cuboid is the sum of the areas of these 6 faces. Hence the surface area of a cuboid is .
What is the surface area of a cuboid?
The surface area is .
There is a cuboid whose base is a square and height is 10 cm. If the area of one side face is , what is the total surface area of the cuboid?
Since the area of one side face is , the side length of the square base is . Thus, the cuboid is a cuboid. Hence, the surface area of the cuboid is
A cuboid's base has an area of , and a perimeter of 20 cm. If the cuboid's height is 6 cm, what is the surface area?
The sum of the areas of the side faces is (perimeter of base) (height), and the surface area of the cuboid is (sum of areas of the side faces) + 2 (area of base). Thus, the surface area of the cuboid is
Consider a cuboid whose base is a rectangle. If the volume of the cuboid is what is the surface area?
An cuboid has a volume of and a surface area of . Since the cuboid's volume is and the base is a rectangle, the height is Then, the surface area of the cuboid is