What is total surface area of cube ?
Suppose we have a cube shape room as mentioned in the below diagram
So total surface area of room includes - length, breadth, height, floor and ceiling of room
As we know that in cube length, breath and height are of equal size, we can say that L=B=H
Total surface area of a cube = 6 (Side)2
Note: Total Surface Area of Cube is always in square units e.g. cm2, m2, mm2 etc
Calculating Total Surface Area of Cube or Surface Area of Cube is one and the same thing. If in a question you are asked to find surface area of cube that means you have to find total surface area of cube.
How formula of total surface area of cube is obtained
Observe the following diagram of cube:
Red lines represent sides of cube
Total surface includes all 6 faces of the cube i.e. left side face, right side face, front face, back face, bottom face and top face (as shown in following four pictures):
Total Surface Area of Cube = Area Left side face + Area of Right side face + Area of Front Face + Area of Back Face + Area of Bottom Face + Area of Top Face ... (Statement 1)
Since all faces 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)
Area of Bottom Face = side2 ... (Statement 6)
Area of Upper Face = side2 ... (Statement 7)
Now put the values of all faces from statement 2, 3, 4, 5, 6 & 7 and put them into statement 1. And we get:
Lateral Surface Area of Cuboid = side2 + side2 + side2 + side2 + side2 + side2
Combining terms and we get:
= 6(side2)
= 6side2
Hence, in this way Total Surface Area of Cube is obtained:
Total Surface Area of Cube = 6side2
Let's try out some example to find total surface area of cube
Example : Find the total surface area of a cube which has a side or edge of 6 cm
Answer :Side of cube = 6 cm (given)
Total surface area of cube = 6 X (side)2
T.S.A. of Cube = 6 X (6)2 cm2
T.S.A. of Cube = 6 X 36 cm2
T.S.A. of Cube = 216 cm2
Example : Find the total surface area of a cube which has a side or edge of 8cm
Answer : Side of cube = 8cm (given)
Total surface area of cube = 6 X (side)2
T.S.A. of Cube = 6 X (8)2 cm2
T.S.A. of Cube = 6 X 64 cm2
T.S.A. of Cube . = 384 cm2
Study More Solved Questions / Examples
Find the total surface area of a cube which has the following sides
A) Side of 9 cm
B) Side of 11 cm
C) Side of 13 cm
D) Side of 17 cm |
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