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Chapter 21: Solids (Surface Area and Volume of 3-D Solids)ICSE Class 9 Maths100% Free

Solids Class 9 ICSE Important Questions with Answers

The 13 questions below are Solids Class 9 ICSE important questions, each with a full step-by-step answer: extra questions beyond the textbook exercises, covering 5 topics of ICSE Class 9 Maths in the question formats used in the exam.

By The Classmate AI Editorial Team

Reviewed by Classmate AI Team · 17 October 2026

Last updated 25 October 2026

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Topics
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Key concepts
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With answers
Quick answer

ICSE Class 9 Solids questions cover the surface area and volume of cubes and cuboids: total and lateral surface area, open and closed boxes, internal and external dimensions, cost of painting or covering, capacity in litres, the longest rod that fits in a room, and volume as area of cross-section ×\times× length, as in a canal or a beam.

Syllabus reference (2026–27): ICSE 2028 Mathematics syllabus (PDF) · CISCE (Council for the Indian School Certificate Examinations)

About Solids (Surface Area and Volume of 3-D Solids)

Inside the ICSE Class 9 Maths chapter Solids (Surface Area and Volume of 3-D Solids) you find the surface area and volume of cubes and cuboids, the two solids in the Class 9 syllabus. You handle open and closed boxes, boxes with a thickness of wood or metal (internal and external dimensions), cost problems, conversion of volume to litres, and the idea that volume equals the area of cross-section multiplied by the length.

Surface area and volume of a cuboidSurface area and volume of a cubeOpen and closed boxes; internal and external dimensionsCost and capacity problemsVolume as area of cross-section × length

Key concepts & formulas

Cuboid

For length lll, breadth bbb, height hhh: total surface area =2(lb+bh+hl)=2(lb+bh+hl)=2(lb+bh+hl), lateral surface area =2h(l+b)=2h(l+b)=2h(l+b), volume =lbh=lbh=lbh, diagonal =l2+b2+h2=\sqrt{l^2+b^2+h^2}=√(l²+b²+h²).

Cube

For edge aaa: total surface area =6a2=6a^2=6a², lateral surface area =4a2=4a^2=4a², volume =a3=a^3=a³, diagonal =a3=a\sqrt3=a√3.

Open box and thickness

An open box has area lb+2h(l+b)lb+2h(l+b)lb+2h(l+b) (no lid). For a box of thickness ttt, each internal dimension is 2t2t2t less than the external one; volume of material === external volume −-- internal volume.

Cross-section

For a solid with a uniform cross-section, volume === area of cross-section ×\times× length. 1 m3=10001\text{ m}^3=10001 m³=1000 litres.

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Solids Questions and Answers

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MCQs with answers (1 mark)

Q1MCQEasy1 mark

The volume of a cube of edge 5 cm5\text{ cm}5 cm is:

  1. (a)

    25 cm325\text{ cm}^325 cm³

  2. (b)

    75 cm375\text{ cm}^375 cm³

  3. (c)

    125 cm3125\text{ cm}^3125 cm³

  4. (d)

    150 cm3150\text{ cm}^3150 cm³

Show model answer

Answer: (c) 125 cm3125\text{ cm}^3125 cm³.

Volume of a cube =a3=53=125 cm3=a^3=5^3=125\text{ cm}^3=a³=5³=125 cm³.

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Q2MCQEasy1 mark

The total surface area of a cuboid 8 cm×5 cm×3 cm8\text{ cm}\times5\text{ cm}\times3\text{ cm}8 cm×5 cm×3 cm is:

  1. (a)

    79 cm279\text{ cm}^279 cm²

  2. (b)

    158 cm2158\text{ cm}^2158 cm²

  3. (c)

    120 cm2120\text{ cm}^2120 cm²

  4. (d)

    188 cm2188\text{ cm}^2188 cm²

Show model answer

Answer: (b) 158 cm2158\text{ cm}^2158 cm².

2(lb+bh+hl)=2(8×5+5×3+3×8)=2(40+15+24)=2(79)=158 cm22(lb+bh+hl)=2(8\times5+5\times3+3\times8)=2(40+15+24)=2(79)=158\text{ cm}^22(lb+bh+hl)=2(8×5+5×3+3×8)=2(40+15+24)=2(79)=158 cm².

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Q3MCQModerate1 mark

The area of metal sheet needed to make an open box (no lid) measuring 10 cm×8 cm×5 cm10\text{ cm}\times8\text{ cm}\times5\text{ cm}10 cm×8 cm×5 cm is:

  1. (a)

    260 cm2260\text{ cm}^2260 cm²

  2. (b)

    340 cm2340\text{ cm}^2340 cm²

  3. (c)

    180 cm2180\text{ cm}^2180 cm²

  4. (d)

    400 cm2400\text{ cm}^2400 cm²

Show model answer

Answer: (a) 260 cm2260\text{ cm}^2260 cm².

An open box has a base and four walls but no top: lb+2h(l+b)=10×8+2×5×(10+8)=80+180=260 cm2lb+2h(l+b)=10\times8+2\times5\times(10+8)=80+180=260\text{ cm}^2lb+2h(l+b)=10×8+2×5×(10+8)=80+180=260 cm². (340 cm2340\text{ cm}^2340 cm² is the closed box, which also has a lid of 80 cm280\text{ cm}^280 cm².)

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Q4MCQHOTS1 mark

If the edge of a cube is doubled, its volume becomes:

  1. (a)

    222 times

  2. (b)

    444 times

  3. (c)

    666 times

  4. (d)

    888 times

Show model answer

Answer: (d) 888 times.

New volume =(2a)3=8a3=(2a)^3=8a^3=(2a)³=8a³, i.e. 888 times the original volume a3a^3a³.

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Assertion–Reason questions (1 mark)

Q5Assertion–ReasonModerate1 mark

Assertion (A): The volume of a cuboid equals the area of its base multiplied by its height.

Reason (R): A cuboid can be thought of as identical rectangular layers, each equal to the base, stacked up to its height.

  1. (a)

    Both A and R are true and R is the correct explanation of A

  2. (b)

    Both A and R are true but R is not the correct explanation of A

  3. (c)

    A is true but R is false

  4. (d)

    A is false but R is true

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Answer: (a) Both A and R are true and R is the correct explanation of A. Stacking layers of area lblblb up to height hhh gives volume lb×hlb\times hlb× h. In general, volume === area of cross-section ×\times× length for any solid with a uniform cross-section.

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Very short answer questions (2 marks)

Q6Very ShortEasy2 marks

The dimensions of a cuboidal water tank are 2 m×1.5 m×1 m2\text{ m}\times1.5\text{ m}\times1\text{ m}2 m×1.5 m×1 m. Find its capacity in litres.

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Volume =lbh=2×1.5×1=3 m3=lbh=2\times1.5\times1=3\text{ m}^3=lbh=2×1.5×1=3 m³.

Since 1 m3=1000 L1\text{ m}^3=1000\text{ L}1 m³=1000 L, capacity =3×1000=3000 L=3\times1000=3000\text{ L}=3×1000=3000 L.

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Q7Very ShortModerate2 marks

Find the length of the longest rod that can be placed in a room 12 m12\text{ m}12 m long, 9 m9\text{ m}9 m broad and 8 m8\text{ m}8 m high.

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The longest rod fits along the space diagonal of the cuboidal room.

Diagonal =l2+b2+h2=122+92+82=144+81+64=289=17 m=\sqrt{l^2+b^2+h^2}=\sqrt{12^2+9^2+8^2}=\sqrt{144+81+64}=\sqrt{289}=17\text{ m}=√(l²+b²+h²)=√(12²+9²+8²)=√(144+81+64)=√289=17 m.

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Short answer questions (3 marks)

Q8Short AnswerModerate3 marks

A room is 10 m10\text{ m}10 m long, 8 m8\text{ m}8 m wide and 4 m4\text{ m}4 m high. Find the cost of painting its four walls and ceiling at Rs 20\text{Rs }20Rs 20 per m2\text{m}^2m² (ignore doors and windows).

Show model answer

Area of four walls =2h(l+b)=2×4×(10+8)=144 m2=2h(l+b)=2\times4\times(10+8)=144\text{ m}^2=2h(l+b)=2×4×(10+8)=144 m².

Area of ceiling =lb=10×8=80 m2=lb=10\times8=80\text{ m}^2=lb=10×8=80 m².

Total area =144+80=224 m2=144+80=224\text{ m}^2=144+80=224 m²; cost =224×20=Rs 4480=224\times20=\text{Rs }4480=224×20=Rs 4480.

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Q9Short AnswerModerate3 marks

The volume of a cube is 343 cm3343\text{ cm}^3343 cm³. Find its edge, total surface area and the length of its diagonal.

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Volume =a3=343⇒a=3433=7 cm=a^3=343\Rightarrow a=\sqrt[3]{343}=7\text{ cm}=a³=343⇒ a=3√343=7 cm.

Total surface area =6a2=6×72=6×49=294 cm2=6a^2=6\times7^2=6\times49=294\text{ cm}^2=6a²=6×7²=6×49=294 cm².

Diagonal =a3=73 cm≈12.12 cm=a\sqrt3=7\sqrt3\text{ cm}\approx12.12\text{ cm}=a√3=7√3 cm≈12.12 cm.

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Q10Short AnswerHOTS3 marks

A canal 50 m50\text{ m}50 m long has a cross-section in the shape of a trapezium, 6 m6\text{ m}6 m wide at the top, 4 m4\text{ m}4 m wide at the bottom and 3 m3\text{ m}3 m deep. How many cubic metres of water can it hold?

Show model answer

Area of cross-section (trapezium) =12×(6+4)×3=15 m2=\dfrac12\times(6+4)\times3=15\text{ m}^2=1/2×(6+4)×3=15 m².

Volume === area of cross-section ×\times× length =15×50=750 m3=15\times50=750\text{ m}^3=15×50=750 m³.

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Long answer questions (5 marks)

Q11Long AnswerModerate5 marks

5 cm5\text{ cm}5 cm of rain falls on a flat roof 20 m20\text{ m}20 m long and 15 m15\text{ m}15 m wide. All the rainwater is collected in a cuboidal tank whose base is 5 m×3 m5\text{ m}\times3\text{ m}5 m×3 m. Find (i) the volume of rainwater in m3\text{m}^3m³ and in litres, (ii) the height to which the water rises in the tank.

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(i) Rainfall =5 cm=0.05 m=5\text{ cm}=0.05\text{ m}=5 cm=0.05 m. Volume =20×15×0.05=15 m3=15×1000=15000=20\times15\times0.05=15\text{ m}^3=15\times1000=15000=20×15×0.05=15 m³=15×1000=15000 litres.

(ii) Volume in the tank === base area ×\times× height: 5×3×h=15⇒h=1 m5\times3\times h=15\Rightarrow h=1\text{ m}5×3× h=15⇒ h=1 m.

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Q12Long AnswerHOTS5 marks

The external dimensions of a closed wooden box are 30 cm×25 cm×20 cm30\text{ cm}\times25\text{ cm}\times20\text{ cm}30 cm×25 cm×20 cm. The wood is 2 cm2\text{ cm}2 cm thick everywhere. Find (i) the internal dimensions, (ii) the internal volume (capacity), and (iii) the volume of wood used to make the box.

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The wood is 2 cm2\text{ cm}2 cm thick on both faces along each dimension, so each internal dimension is 2×2=4 cm2\times2=4\text{ cm}2×2=4 cm less than the external.

(i) Internal dimensions:

length =30−4=26 cm=30-4=26\text{ cm}=30-4=26 cm, breadth =25−4=21 cm=25-4=21\text{ cm}=25-4=21 cm, height =20−4=16 cm=20-4=16\text{ cm}=20-4=16 cm.

(ii) Internal volume (capacity) =26×21×16=8736 cm3=26\times21\times16=8736\text{ cm}^3=26×21×16=8736 cm³.

(iii) External volume =30×25×20=15000 cm3=30\times25\times20=15000\text{ cm}^3=30×25×20=15000 cm³.

Volume of wood === external volume −-- internal volume =15000−8736=6264 cm3=15000-8736=6264\text{ cm}^3=15000-8736=6264 cm³.

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Case study questions (4 marks)

Q13Case-basedModerate4 marks

Read the passage and answer the questions.

The overhead water tank of an apartment block is a cuboid with internal dimensions 4 m×2.5 m×1.5 m4\text{ m}\times2.5\text{ m}\times1.5\text{ m}4 m×2.5 m×1.5 m, and it has no lid. Each flat uses about 750750750 litres of water a day.

(i) Find the capacity of the tank in m3\text{m}^3m³.

(ii) Express this in litres.

(iii) A full tank meets the daily need of how many flats?

(iv) Find the cost of painting the inside of the tank (base and four walls) at Rs 50\text{Rs }50Rs 50 per m2\text{m}^2m².

Show model answer

(i) 4×2.5×1.5=15 m34\times2.5\times1.5=15\text{ m}^34×2.5×1.5=15 m³.

(ii) 15×1000=1500015\times1000=1500015×1000=15000 litres.

(iii) 15000750=20\dfrac{15000}{750}=2015000/750=20 flats.

(iv) Area =lb+2h(l+b)=4×2.5+2×1.5×(4+2.5)=10+19.5=29.5 m2=lb+2h(l+b)=4\times2.5+2\times1.5\times(4+2.5)=10+19.5=29.5\text{ m}^2=lb+2h(l+b)=4×2.5+2×1.5×(4+2.5)=10+19.5=29.5 m²; cost =29.5×50=Rs 1475=29.5\times50=\text{Rs }1475=29.5×50=Rs 1475.

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Continues in Class 10: Cylinder, Cone and Sphere Class 10 ICSE questions

All ICSE Class 9 Maths Chapters

Rational and Irrational NumbersCompound Interest (Without Using Formula)Compound Interest (Using Formula)ExpansionsFactorisationSimultaneous (Linear) EquationsIndices (Exponents)LogarithmsTriangles (Congruency in Triangles)Isosceles TrianglesInequalitiesMid-point and Its Converse (Including Intercept Theorem)Pythagoras TheoremRectilinear Figures (Quadrilaterals)Construction of PolygonsArea TheoremsCircleStatistics (Classification of Data, Tabulation)Mean and MedianArea and Perimeter of Plane FiguresSolids (Surface Area and Volume of 3-D Solids)Trigonometrical RatiosTrigonometrical Ratios of Standard AnglesSolution of Right TrianglesComplementary AnglesCo-ordinate GeometryGraphical Solution (Simultaneous Linear Equations, Graphically)Distance Formula

Frequently asked questions

  • What are the important questions in Solids ICSE Class 9?
    Surface area and volume of cubes and cuboids, open boxes, internal and external dimensions, cost of painting, capacity in litres, the longest rod in a room, and solids with a uniform cross-section such as canals. This page on Solids (Surface Area and Volume of 3-D Solids) has 13 of them, each with a worked answer.
  • How do you find the total surface area and diagonal of a cuboid?
    Total surface area =2(lb+bh+hl)=2(lb+bh+hl)=2(lb+bh+hl) and diagonal =l2+b2+h2=\sqrt{l^2+b^2+h^2}=√(l²+b²+h²). For 8×5×38\times5\times38×5×3 cm, the surface area is 2(40+15+24)=158 cm22(40+15+24)=158\ \text{cm}^22(40+15+24)=158 cm². The diagonal is the longest rod that fits inside.
  • How many litres does a 2 m × 1.5 m × 1 m tank hold?
    Its volume is 2×1.5×1=3 m32\times1.5\times1=3\ \text{m}^32×1.5×1=3 m³, and 1 m3=10001\ \text{m}^3=10001 m³=1000 litres, so it holds 300030003000 litres. Convert to cubic metres first, then to litres. For smaller vessels, remember that 1000extcm31000 ext{cm}^31000 extcm³ is one litre.
  • How much rainwater falls on a roof?
    Multiply the roof area by the rain depth in metres. 555 cm of rain on a 202020 m by 151515 m roof is 300×0.05=15 m3300\times0.05=15\ \text{m}^3300×0.05=15 m³, or 150001500015000 litres. This page's 5-mark question then pours it into a tank.
  • Which ICSE chapter covers cylinders, cones and spheres?
    Class 10's Cylinder, Cone and Sphere (Chapter 20). In Class 9, Solids is Chapter 21, after Area and Perimeter of Plane Figures (Chapter 20). Both sit next to Solids (Surface Area and Volume of 3-D Solids) in this site's chapter list.
  • How do I handle thickness in box problems?
    Subtract twice the thickness from each external dimension to get the internal ones (only once for height if the box is open). The volume of wood is external volume minus internal volume. Forgetting the factor of 222 is the usual slip.
  • Can I download Solids surface area and volume ICSE questions?
    Yes. Enter your email in the free PDF box on this page to open all 13 cube and cuboid questions with worked answers as a printable worksheet.

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