Surface Area Of A Cube
To derive the formula of the surface area of a cube, you will need to start with a cube as shown below and call the length of one side a.
In order to make a cube like the one shown above, you basically use the following cube template:
Looking at the cube template, it is easy to see that the cube has six sides and each side is a square
The area of one square is a × a = a2
Since there are six sides, the total surface area, call it SA is:
SA = a2 + a2 + a2 + a2 + a2 + a2
SA = 6 × a2
Find the surface area if the length of one side is 3 cm.
Surface area = 6 × a2
Surface area = 6 × 32
Surface area = 6 × 3 × 3
Surface area = 54 cm2
Surface Area of a Cuboid
The total surface area (TSA) of a cuboid is the sum of the areas of its 6 faces, which is given by:
TSA = 2 (lw + wh + hl)
Remember the surface area is the total area of all the faces of a 3D shape.
The lateral surface area of a cuboid is given by:
LSA = 2 (lh + wh) = 2 h (l + w)
Find the surface area of a cuboid of dimensions 4.8 cm, 3.4 cm and 7.2 cm.
Area of Face 1: 4.8 × 7.2 = 34.56 cm²
Area of Face 2: 3.4 × 7.2 = 24.48 cm²
Area of Face 3: 4.8 × 3.4 = 16.32 cm²
Adding the area of these 3 faces gives 75.36 cm², since each face is duplicated on the opposite side, the total surface area of the cuboid will be:
TSA = 2 (75.36) = 150.72 cm²
Surface area of a cylinder
Definition: The number of square units it takes to exactly cover the surface of a cylinder. Given by the formula:
π is Pi, approximately 3.142
r is the radius of the cylinder
h height of the cylinder
The surface area of a cylinder can be found by breaking it down into three parts:
- The two circles that make up the ends of the cylinder.
- The side of the cylinder, which when "unrolled" is a rectangle
Combining these parts we get the formula: