Exercise 14.1 — Surface Area
Total surface area and lateral surface area of cube and cuboid.
Surface Area and Volume — Cube & Cuboid
Exercise 14.1 solved step by step with diagrams, formulas and tips — for CBSE, Telangana SCERT & Andhra Pradesh students.
What is Exercise 14.1 About?
Exercise 14.1 of Class 8 Mathematics, Chapter 14 — Surface Area and Volume — introduces two important measurements for solid shapes: the Total Surface Area (TSA) and the Lateral Surface Area (LSA) of a cuboid and a cube. These ideas come up constantly in real life — from figuring out how much cardboard is needed to make a box, to calculating how much paint is required to cover a cupboard or a water tank.
This exercise has four questions. The first asks you to compare two boxes and decide which needs less material. The second works backwards — given the surface area, you find the side of a cube. The third introduces the idea of painting only some faces of a cuboid (LSA), and the fourth combines surface area with a real-world cost calculation. Together, these four problems give you a complete toolkit for solving any TSA/LSA question in your CBSE, Telangana, or Andhra Pradesh board exam.
• TSA of a cuboid =
2(lb + bh + hl)• TSA of a cube =
6l²• LSA of a cuboid =
2h(l + b)
Cuboid vs Cube — What's the Difference?
A cuboid is a box-like solid with three dimensions — length (l), breadth (b), and height (h) — which are usually all different. It has six rectangular faces, arranged in three pairs of identical rectangles. A cube is a special case of a cuboid where length, breadth, and height are all equal (l = b = h), so all six faces are identical squares.
The Total Surface Area (TSA) is simply the sum of the areas of all six faces — useful when an object (like a box) is covered or painted on every side. The Lateral Surface Area (LSA) only counts the four "side" faces, leaving out the top and bottom — useful when, say, only the walls of a room (and not the floor or ceiling) need to be painted.
2 × (l × b)2 × (l × h)2 × (b × h)TSA of cuboid = 2(lb + bh + hl)TSA of cube = 6l² (since l = b = h)LSA of cuboid = 2h(l + b) (excludes top and bottom faces)Question 1 — Which Box Needs Less Material?
The question gives two cuboidal boxes. Fig A is a cuboid with length 60 units, breadth 40 units, and height 50 units. Fig B is a cube with every edge equal to 50 units. We need to find the Total Surface Area of each box — since the amount of material needed to build a box is directly proportional to its surface area — and then compare the two values.
| Box | Shape | Dimensions | Total Surface Area |
|---|---|---|---|
| Fig A | Cuboid | 60 × 40 × 50 units | 14,800 sq. units |
| Fig B | Cube | 50 × 50 × 50 units | 15,000 sq. units |
Question 2 — Finding the Side of a Cube from Its Surface Area
This question reverses the process. Instead of being given the side of a cube and asked to find its surface area, we're told the Total Surface Area is 600 cm² and must find the side length. This is solved by substituting into the cube's TSA formula and then taking a square root.
l² = 100 requires finding a square root. If you'd like more practice with square roots (and their use in geometry problems like this one), revisit Square Roots and Cube Roots — it's the same skill applied here.
Question 3 — Prameela's Cabinet (Lateral Surface Area)
Prameela paints the outer surface of a cuboidal cabinet that measures 1 m × 2 m × 1.5 m (length × breadth × height). However, she paints all faces except the top and bottom — that means only the four "wall-like" side faces are painted. This is exactly what the Lateral Surface Area (LSA) formula measures.
2(lb + bh + hl) includes the top and bottom faces (the two lb terms). Since Prameela skips those two faces, we drop the 2lb part entirely, leaving 2(bh + hl) = 2h(l + b) — the Lateral Surface Area.
Question 4 — Cost of Painting a Cuboid
This question combines two ideas: finding the Total Surface Area of a cuboid, and then using it to calculate a real-world cost. A cuboid measuring 20 cm × 15 cm × 12 cm is to be painted on all faces at a rate of 5 paise per square centimetre. We first find the TSA, then multiply by the rate.
Common Mistakes to Avoid
- Mixing up TSA and LSA: If a question says "all faces" or "outer surface", use TSA =
2(lb + bh + hl). If it excludes the top/bottom (like Question 3), use LSA =2h(l + b). - Forgetting the factor of 2: Surface area formulas account for pairs of faces. Leaving out the "2" gives an answer that is exactly half the correct one.
- Confusing units: Surface area is measured in square units (sq. cm, sq. m), while side lengths are in plain units (cm, m). When you find
l = √100 = 10, the answer is in cm, not sq. cm. - Currency conversion slip-ups: Remember that 100 paise = ₹1. A cost of 7,200 paise must be divided by 100 to get ₹72 — a very common place to lose marks.
- Arithmetic order errors: When computing
2(lb + bh + hl), calculate each product (lb,bh,hl) separately first, add them, and only then multiply by 2.
TSA = 6l instead of TSA = 6l². Since surface area is a two-dimensional quantity, the side length must always be squared.
Quick Reference — All Answers at a Glance
| Question | Given | Formula Used | Final Answer |
|---|---|---|---|
| Q1 | Fig A: 60×40×50; Fig B: cube of side 50 | TSA cuboid & TSA cube | Fig A (14,800) needs less material than Fig B (15,000) |
| Q2 | TSA of cube = 600 cm² | 6l² = TSA, then l = √(TSA ÷ 6) | l = 10 cm |
| Q3 | l = 1 m, b = 2 m, h = 1.5 m (top & bottom unpainted) | LSA = 2h(l + b) | 9 sq. m |
| Q4 | 20 cm × 15 cm × 12 cm, rate = 5 paise/cm² | TSA = 2(lh+bh+lb), Cost = TSA × rate | TSA = 1,440 sq. cm; Cost = ₹72 |
What This Lesson Prepares You For
Mastering TSA and LSA of cuboids and cubes is the launching pad for the rest of Chapter 14. Once surface area feels comfortable, the natural next step is Volume — measuring how much space a cuboid or cube can hold, using the formula V = l × b × h (or V = l³ for a cube). You can continue with Exercise 14.2 — Volume of Cube and Cuboid to build on what you've learned here.
Question 2 of this exercise also showed how square roots are used to "undo" a squared formula. If finding l = √100 felt unfamiliar, a quick revision of Square Roots and Cube Roots will make these reverse problems much easier — and the same idea (using a cube root instead of a square root) reappears when finding the side of a cube from its volume.