Surface Area — TSA & LSA of Cubes & Cuboids explained through a friendly whiteboard conversation, examples, visuals, and practice for school students.
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Notes
Step 2
Formulae
Step 3
Examples
Step 4
Practice
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Surface area measures the total area of faces on a 3D solid.
For cubes and cuboids, students often calculate total surface area and lateral surface area.
These ideas are used for painting, wrapping, covering, and making boxes.
A cuboid has six rectangular faces. Surface area is found by adding the areas of these faces.
Total surface area, or TSA, includes all faces.
Lateral surface area, or LSA, includes the side faces but not the top and bottom.
A cube has six equal square faces, so its formulas are shorter.
Cost problems usually multiply area by cost per square unit.
Meaning: TSA includes all six faces of a cuboid.
Definition: TSA of cuboi(lh).
There are two faces of each type: lengtreadth, breadteight, and lengteight.
Meaning: LSA includes only the four side faces.
Definition: LSA of cuboih().
It is useful for painting four walls of a room without floor and ceiling.
Meaning: A cube has six equal square faces.
Definition: TSA of cub and LSA of cub.
If side is 5 cm, TS x c.
Meaning: Cost depends on the area being covered.
Definition: Total cosrea x cost per square unit.
If area is 80 and cost is Rs 12 per , total coss 960.
Easy
Question: Find the TSA of a cube with side 4 cm.
Medium
Question: Find the LSA of a cuboid with length 8 cm, breadth 5 cm, and height 6 cm.
Exam-level
Question: A room is 10 m long, 6 m broad, and 4 m high. Find the cost of painting four walls at Rs 20 per .
Using volume formula for surface area
Why it happens: Both use length, breadth, and height.
Correct approach: Surface area adds face areas. Volume multiplies three dimensions.
Using TSA when only four walls are painted
Why it happens: All faces are included by habit.
Correct approach: Use LSA for four side faces.
Writing cubic units for surface area
Why it happens: The topic is 3D solids.
Correct approach: Surface area uses square units.
What is the difference between TSA and LSA?
TSA includes all faces. LSA includes only side faces.
Which area is used for painting four walls?
Use lateral surface area of the room.
Why is surface area not in cubic units?
Surface area measures faces, which are 2D, so it uses square units.
Practise the same concept from this article. Your student profile may guide entitlement and follop recommendations, but it does not replace this concept.