If we want to calculate the area of a cube then it’s always better to see each surface as a square and a cube is made up of six equal squares. Considering each side of the square as “a”, then the area of each square will be a2. Therefore, the surface area of the cube will be 6a2.
Surface area<span> is the measure of how much exposed of area a solid object has, expressed in square units. Mathematical description of the surface area is considerably more involved than the definition of arc length of a curve. For polyhedra (objects with flat polygonal faces) the surface area is the sum of the areas of its faces. A cube is called a hexahedron because it is a polyhedron that has 6 (</span>hexa-<span> means 6) faces. The sum of the areas of all external surfaces of a three-dimensional object is called its total surface area (</span>TSA<span>).
The longest diagonal of the cube (i.e., the line joining one vertex on the top face to the diagonally opposite vertex on the bottom face) is called the diagonal of the cube. The length of the diagonal of the cube is 3√(a) and The lateral surface area of a cube = 4 a</span>2.
Example 1<span>: Find the surface area if the length of one side is 1/2 cm. </span> Solution<span>: </span> <span>SA = 6 × a2 </span> <span>SA = 6 × (1/2)2 </span> <span>SA = 6 × 1/2 × 1/2 </span> <span>SA = 6 × 1/4 </span> <span>SA = 1.5 cm2 </span>
Example 2: Find the Surface area of a cube of side length 8 cm. Solution<span>: </span> <span>SA = 6 × a2</span> <span>SA = 6 × (8)2</span> SA = 6 × (64) <span>SA = 384 cm2</span>
Example 3: Find the total surface area of a box whose edges are all 4.5 cm long. Solution<span>: </span>
