What is a lateral face ?
Faces that meet the base are called lateral faces of cube. ( What are Faces in Cube ? )
What is lateral surface area of cube or Curved Surface Area of Cube ?
Suppose we have a cube shape room as mentioned in the below diagram
So lateral surface area of room includes - length, breadth and height of room (we donot include ceiling and floor) and as we know that in cube length, breadth and height are of equal size, we can say that -
Lateral surface area of cube = 4 (side)2
Note: Lateral Surface Area of Cylinder is always in square units e.g. cm2, m2, mm2 etc
How formula of lateral surface area of cube is obtained
Observe the following diagram of cube:
Red lines represent sides of cube
Lateral surface includes 4 faces of the cube i.e. left side face, right side face, front face and back face (as shown in following four pictures):
Lateral Surface Area of Cube = Area Left side face + Area of Right side face + Area of Front Face + Area of Back Face ... (Statement 1)
Since all faces are in the shape of square, so to find area of faces; apply formula of area of square and we get:
Area of Left Face = side2 ... (statement 2)
Area of Right Side Face = side2 ... (Statement 3)
Area of Front Face = side2 ... (Statement 4)
Area of Back face = side2 ... (Statement 5)
Now put the values of all faces from statement 2, 3, 4 & 5 and put them into statement 1. And we get:
Lateral Surface Area of Cube = side2 + side2 + side2 + side2
Combining terms and we get:
Lateral Surface Area of Cube = 4 (side2)
Hence, in this way Lateral Surface Area of Cube is obtained:
Let's try some examples to find Lateral surface area of cube
Example 1 - Find the lateral surface area of a cube which has a side or edge of 6 cm
Solution :
Side of Cube = 6 cm (given)
Lateral surface area of cube = 4(side)2
L.S.A. of Cube = 4 (6)2
L.S.A. of Cube = 4 (36)
L.S.A. of Cube = 144 cm2
Example 2 - Find the lateral surface area of a cube which has a side or edge of 8 cm
Solution :
Side of Cube = 8 cm (given)
Lateral surface area of cube = 4(side)2
L.S.A. of Cube = 4 (8)2
L.S.A. of Cube = 4 (64)
L.S.A. of Cube = 256 cm2
Example 3 - Find the lateral surface area of a cube which has a side or edge of 12 cm
Solution :
Side of Cube = 12 cm (given)
Lateral surface area of cube = 4(side)2
L.S.A. of Cube = 4 (12)2
L.S.A. of Cube = 4 (144)
L.S.A. of Cube = 576 cm2
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