Question

The total surface area of cuboid of length \(l\), breadth \(b\), height \(h\) is _____.

• A. \(2(lb + bh + hl)\)
• B. \(2h(l+b)\)
• C. \(lbh\)
• D. \(lb+bh+hl\)

Hint:

Remember: \[ \text{Cuboid TSA} = 2(lb + bh + hl) \] and: \[ \text{Cuboid Volume} = lbh \] Students often confuse TSA with volume, so always check whether the question asks for “surface area” or “volume”.

Answer 1

The Correct Option is A

Concept: A cuboid is a three-dimensional solid having:
• Length \(= l\)
• Breadth \(= b\)
• Height \(= h\) A cuboid has:
• 6 rectangular faces
• Opposite faces are equal in area The total surface area (TSA) means the sum of the areas of all six faces.

Step 1: Identify all pairs of faces. A cuboid has three different types of rectangular faces:
• Top and bottom faces: \[ \text{Area of each} = l \times b \] Since there are two such faces: \[ 2lb \]
• Front and back faces: \[ \text{Area of each} = l \times h \] Since there are two such faces: \[ 2lh \]
• Left and right faces: \[ \text{Area of each} = b \times h \] Since there are two such faces: \[ 2bh \]

Step 2: Add all face areas. \[ \text{TSA} = 2lb + 2lh + 2bh \] Take common factor 2: \[ \text{TSA} = 2(lb + lh + bh) \] Rearranging terms: \[ \boxed{2(lb + bh + hl)} \]

Step 3: Verify the options. Option (1): \[ 2(lb + bh + hl) \] matches the correct formula. Final Answer: \[ \boxed{2(lb + bh + hl)} \]