What is total surface area of cuboid ?
Suppose we have a cuboid shape room like as below
So total surface area of room includes - length, breadth, height, floor and ceiling of room.
so the formula to find the total surface area of cuboid = 2 [LB + BH + HL]
or in other words : A cuboid has 6 rectangular faces, so the area of all 6 rectangular faces will be the total surface area of cuboid.
Calculating Total Surface Area of Cuboid or Surface Area of Cuboid is one and the same thing. If in a question you are asked to find surface area of cuboid that means you have to find the total surface area of cuboid.
How formula for total surface area of cuboid is obtained
Observe the following diagram of cuboid:
Red lines represent length of cuboid (L)
Green lines represent breadth of cuboid (B)
Blue lines represent height of cuboid (H)
Total surface includes all 6 faces of the cuboid i.e. left side face, right side face, front face, back face, bottom face and upper face (as shown in following four pictures):
Total Surface Area of Cuboid = Area Left side face + Area of Right side face + Area of Front Face + Area of Back Face + Area of Bottom Face + Area of Upper Face ... (Statement 1)
Since all face in the shape of rectangle, so to find area of faces; apply formula of area of rectangle and we get:
Area of Left Face = Length X breadth
As shown in the diagram, length = height, so we get:
Area of Left Face = height X breadth = h X b ... (Statement 2)
Similarly, Area of Right Side Face = h X b ... (Statement 3)
Area of Front Face = L X H ... (Statement 4)
Area of Back face = L X H ... (Statement 5)
Area of Bottom Face = L X B ... (Statement 6)
Area of Upper Face = L X B ... (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 = (H X B) + (H X B) + (L X H) + (L X H) + (L X B) + (L X B)
Combining terms and we get:
=2(H X B) + 2(L X H) + 2(L X B)
Taking common terms and we get:
= 2(BH + LH + LB)
Hence, in this way Lateral Surface Area of Cuboid is obtained:
Lateral Surface Area of Cuboid = 2(BH + LH + LB)
Note: Total Surface Area of Cuboid is always in square units e.g. cm2, m2, mm2 etc
Let's try out some examples to find total surface area of Cuboid
Example 1 :A plastic box is 1.5m long, 1.25m wide and 65cm deep, Ignoring the thickness of plastic box, calculate its total surface area
Answer: Below things are given in the example
Length = 1.5m
Breadth = 1.25m
Height(depth) = 0.65m [i.e. 65cm = 0.65m]
Total surface area of cuboid is = 2[LB + BH + HL]
T.S.A of cuboid = 2[1.5 X 1.25 + 1.25 X 0.65 + 0.65 X 1.5] m2
T.S.A of cuboid = 2[1.87 + 0.81 + 0.97] m2
T.S.A of cuboid = 2 X 3.65 m2
T.S.A of cuboid = 7.30 m2
Example 2 : A small green house is made up of glass planes including its base. The dimensions are 30cm long, 25cm wide and 35cm high. Ignoring the thickness of glass planes, Calculate the total surface area of greenhouse
Answer: Below things are given in the example
Length = 30cm
Breadth = 25cm
Height = 35cm
Total surface area of cuboid is = 2[LB + BH + HL]
T.S.A of cuboid = 2[30 X 25 + 25 X 35 + 35 X 30] cm2
T.S.A of cuboid = 2[750 + 875 + 1050] cm2
T.S.A of cuboid = 2 X 2675 cm2
T.S.A of cuboid = 5350 cm2
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