MathsICSE Class 8 · Surface Area and Volume

Total, Lateral and Curved Surface Area of a Cuboid, Cube and Cylinder (ICSE Class 8)

Updated 17 October 2026 · Fact-checked

Cuboid: TSA $= 2(lb + bh + hl)$, LSA $= 2h(l + b)$. Cube of side $a$: TSA $= 6a^2$, LSA $= 4a^2$. Cylinder: CSA $= 2\pi r h$, TSA $= 2\pi r(r + h)$. An open box or a room without floor or ceiling needs fewer faces.

Understand Surface Area of a Cuboid, Cube and Cylinder

The CISCE curriculum covers the surface area of a cube, cuboid and cylinder, with the idea of total and curved surface areas.

Cuboid ( $l \times b \times h$ ): six rectangular faces in three equal pairs.

Total surface area (TSA) $= 2 (l b + bh + h l)$ .
Lateral surface area (LSA, the four walls) $= 2 h (l + b)$ .

Cube (side $a$ ): TSA $= 6 a^{2}$ ; LSA $= 4 a^{2}$ .

Cylinder (radius $r$ , height $h$ ): the curved surface opens into a rectangle of width $2 π r$ and height $h$ .

Curved surface area (CSA) $= 2 π r h$ .
Total surface area $= 2 π r h + 2 π r^{2} = 2 π r (h + r)$ .

Choosing the right faces. A room needs paint on 4 walls (LSA) and maybe the ceiling; an open tank has no top; a closed box has all six faces; a tin may have a top and bottom of circular shape. Subtract doors and windows from walls.

Joining solids. When two solids are glued, the covered faces disappear: two cubes of side $4$ joined face-to-face have TSA $160$ , while separately they have $2 \times 96 = 192$ .

Working backwards. For a cylinder with CSA and height known, $r = \frac{CSA}{2 π h}$ .

Units. Area in square units; check that $l, b, h$ are in the same unit.

Surface Area of a Cuboid, Cube and Cylinder: formulas to remember

Cuboid: $T S A = 2 (l b + bh + h l), L S A = 2 h (l + b)$; LSA is the four walls.
Cube: $T S A = 6 a^{2}, L S A = 4 a^{2}$; Special case of cuboid.
Cylinder: $C S A = 2 π r h, T S A = 2 π r (r + h)$; Open at one end: CSA + $π r^{2}$ .

How to solve Surface Area of a Cuboid, Cube and Cylinder questions

Decide which faces are included, then apply the formula face by face.

1Sketch the solid and decide which faces are included.
2Write the formula for those faces.
3Substitute with the same units throughout.
4Subtract any openings; add costs by area if asked.
5State the answer in square units.

Surface Area of a Cuboid, Cube and Cylinder in real life

Each concept, met in an everyday situation. Read the situation, try the problem, then check the solution. The one-line hook is what to remember.

Painting a room

Suppose a room is 8 m long, 6 m wide and 3.5 m high, with one door 2 m by 1 m and one window 1 m by 1 m. Only the four walls are to be painted at Rs 20 per square metre.

Find the cost of painting.

Try it first, then show the solutionSolution

Walls $= 2 \times 3.5 \times (8 + 6) = 98$ m $^{2}$ .
Openings $= 2 + 1 = 3$ m $^{2}$ ; to paint $= 95$ m $^{2}$ ; cost $= 95 \times 20 = 1900$ .

Answer: Rs 1,900.

Memory hook: Four walls: 2h(l + b), minus doors and windows.

Tricks to remember Surface Area of a Cuboid, Cube and Cylinder

Short memory aids. Say each one aloud once, then use it on a question the same day.

Pairs of faces
A cuboid has 3 pairs of equal faces; add the three areas and double.
Use it when: Cuboid TSA.
Rectangle from curve
A cylinder's curved surface unrolls into a rectangle of size circumference by height.
Use it when: Cylinder CSA.

Surface Area of a Cuboid, Cube and Cylinder: solved examples

Ordered from board level to HOTS. Try each one before you open the solution.

Example 1: Cube · 1 mark · MCQBoard level

The total surface area of a cube of side 6 cm is:
(a) 36 cm $^{2}$ (b) 216 cm $^{2}$ (c) 144 cm $^{2}$ (d) 72 cm $^{2}$

Try it first, then show the solutionSolution

$6 a^{2} = 6 \times 36 = 216$ .

Answer: (b)

Example 2: Cuboid TSA and LSA · 3 marks · Short answerBoard level

A cuboid measures 12 cm by 8 cm by 5 cm. Find its total surface area and its lateral surface area.

Try it first, then show the solutionSolution

TSA $= 2 (12 \times 8 + 8 \times 5 + 5 \times 12) = 2 (96 + 40 + 60) = 392$ cm $^{2}$ .
LSA $= 2 \times 5 \times (12 + 8) = 200$ cm $^{2}$ .

Answer: TSA 392 cm $^{2}$ ; LSA 200 cm $^{2}$

Example 3: Painting walls · 3 marks · Short answerHarder board level

A room is 8 m by 6 m and 3.5 m high. It has a door 2 m by 1 m and a window 1 m by 1 m. Find the cost of painting only the four walls at Rs 20 per m $^{2}$ .

Try it first, then show the solutionSolution

Walls $= 2 \times 3.5 \times 14 = 98$ m $^{2}$ .
Minus openings $2 + 1 = 3$ : $95$ m $^{2}$ .
Cost $= 95 \times 20 = 1900$ .

Answer: Rs 1,900

Example 4: Cylinder · 4 marks · Short answerHarder board level

A cylinder has radius 7 cm and height 10 cm. Find its curved surface area and its total surface area.

Try it first, then show the solutionSolution

CSA $= 2 \times \frac{22}{7} \times 7 \times 10 = 440$ cm $^{2}$ .
Each circular end $= \frac{22}{7} \times 49 = 154$ ; two ends $= 308$ .
TSA $= 440 + 308 = 748$ cm $^{2}$ .

Answer: CSA 440 cm $^{2}$ ; TSA 748 cm $^{2}$

Example 5: Joined cubes · 4 marks · Long answerHOTS / competency

Two cubes of side 4 cm are joined face to face to make a cuboid. Find the total surface area of the cuboid and the area that disappears compared with the two separate cubes.

Try it first, then show the solutionSolution

The cuboid is $8 \times 4 \times 4$ : TSA $= 2 (32 + 32 + 16) = 160$ cm $^{2}$ .
Two separate cubes: $2 \times 6 \times 16 = 192$ cm $^{2}$ .
Lost area $= 192 - 160 = 32$ cm $^{2}$ (two glued faces of $16$ each).

Answer: 160 cm $^{2}$ ; 32 cm $^{2}$ lost

Where students lose marks in Surface Area of a Cuboid, Cube and Cylinder

The slips examiners see most often, and what to write instead.

Mistake: Using the total surface area for painting four walls
Only the lateral faces are painted.
Wrong working
Room $8 \times 6 \times 3.5$ : area $= 2 (48 + 21 + 28) = 194$ .
Right working
Walls $= 2 \times 3.5 \times 14 = 98$ .
Do this: List the faces needed first.
Usually costs: Answer mark.
Mistake: Forgetting the two circular ends in the total surface area of a cylinder
TSA includes both ends.
Wrong working
TSA $= 2 π r h$ .
Right working
TSA $= 2 π r h + 2 π r^{2}$ .
Do this: CSA is only the curved part.
Usually costs: Answer mark.

Exam tips

State which faces are included before using a formula.
Check that l, b and h are in the same unit.
Write units as cm $^{2}$ or m $^{2}$ .

Practice questions on Surface Area of a Cuboid, Cube and Cylinder

Write each answer on paper first. Open the hint only if you are stuck, and the answer only when you have finished.

Q1 · 1 mark · MCQBoard level
The lateral surface area of a cuboid with length $l$ , breadth $b$ and height $h$ is:
(a) $2 (l b + bh + h l)$ (b) $l bh$ (c) $2 h (l + b)$ (d) $4 l b$
Hint
Four walls only.
Answer
(c)
Q2 · 2 marks · Short answerBoard level
Find the total and lateral surface areas of a cube of side 9 cm.
Hint
6a^2 and 4a^2.
Answer
TSA $= 6 \times 81 = 486$ cm $^{2}$ ; LSA $= 4 \times 81 = 324$ cm $^{2}$ .
Q3 · 3 marks · Short answerHarder board level
A closed box measures 40 cm by 30 cm by 20 cm. Find the area of material needed for the closed box and for an open box (no top).
Hint
Subtract the top face.
Answer
Closed: $2 (1200 + 600 + 800) = 5200$ cm $^{2}$ . Open top: subtract $40 \times 30 = 1200$ , giving $4000$ cm $^{2}$ .
Q4 · 3 marks · Short answerHarder board level
A cylinder has radius 3.5 cm and height 12 cm. Find its curved and total surface areas.
Hint
Use 22/7.
Answer
CSA $= 2 \times \frac{22}{7} \times 3.5 \times 12 = 264$ cm $^{2}$ . Ends: $2 \times \frac{22}{7} \times 12.25 = 77$ . TSA $= 341$ cm $^{2}$ .
Q5 · 4 marks · Long answerHOTS / competency
The curved surface area of a cylindrical drum is 1320 cm $^{2}$ and its height is 15 cm. Find its radius and its total surface area.
Hint
CSA gives the radius.
Answer
$2 \times \frac{22}{7} \times r \times 15 = 1320 \Rightarrow r = 14$ cm. Each end $= \frac{22}{7} \times 196 = 616$ ; TSA $= 1320 + 1232 = 2552$ cm $^{2}$ .

Test your recall

Answer in your head or on paper first, then open the card. Pulling an answer out of memory makes it stick far better than re-reading.

1.TSA of a cuboid?Show answer
2(lb + bh + hl).
2.LSA of a cube?Show answer
4a^2.
3.CSA of a cylinder?Show answer
2 pi r h.
4.Does a room paint include the floor?Show answer
Only if the question says so.

Surface Area of a Cuboid, Cube and Cylinder: frequently asked questions

What is the difference between LSA and CSA?

LSA is the sum of side faces of a cuboid or cube; CSA is the curved face of a cylinder.

Does an open tank have a top?

No; omit the top face.