Class 9 Maths Surface Areas and Volumes MCQs with Detailed Answers and Explanations

Improve Mensuration Skills with Surface Areas and Volumes MCQ Practice

Surface Areas and Volumes is one of the most calculation intensive chapters in Class 9 Maths. Unlike basic geometry chapters that focus mainly on shapes and properties, this chapter introduces students to three dimensional figures and teaches how to measure the space occupied by solids along with their outer covering area.

In this chapter, students work with cubes, cuboids, cylinders, cones, and spheres using formulas related to area and volume. The questions are highly practical because they involve real measurement concepts connected to containers, storage capacity, surface covering, and space calculation.

This page on Class 9 Maths Surface Areas and Volumes MCQs with Answers and explanations is designed for students who want to improve formula application, calculation accuracy, and numerical problem solving through objective practice. The MCQs included here are based on CBSE and NCERT concepts and help students strengthen mensuration fundamentals step by step.

Many students understand formulas theoretically but struggle while solving numerical questions involving units, radius, height, diameter, and conversion based calculations. Regular practice of Surface Areas and Volumes Class 9 MCQ questions helps students improve calculation speed and reduces mistakes during exams.

Students preparing for complete chapter wise revision can also explore the CBSE Class 9 Maths, practice concept wise exercises from the Class 9 Maths Course, and solve additional objective questions available in the Maths MCQs Collection.

Why Surface Areas and Volumes is a High Scoring Chapter

This chapter is considered scoring because most questions are formula based and follow a direct solving approach. Students who remember formulas correctly and practice calculations regularly can score very well in examinations.

The chapter also helps students:

Improve mensuration calculation skills

Strengthen formula application ability

Build confidence in numerical problem solving

Understand practical measurement concepts

Improve unit conversion accuracy

Develop step based mathematical thinking

Students who practice numerical questions consistently usually solve mensuration problems much faster in exams.

What Concepts are Covered in Chapter 11

Chapter 11 mainly focuses on finding the surface area and volume of different solid shapes using standard mathematical formulas.

Important concepts included in this chapter are:

Surface area of cubes and cuboids

Volume of cubes and cuboids

Curved surface area of cylinders and cones

Total surface area calculations

Volume of cylinders and cones

Sphere and hemisphere formulas

Unit conversion problems

Application based mensuration questions

Regular practice of Class 9 Maths Chapter 11 MCQs helps students improve both conceptual understanding and numerical accuracy.

Important Formula Revision Table

Students should revise formulas regularly before attempting objective questions.

Surface Areas and Volumes MCQs with Answers and Explanations

Q. The surface area of a cube is 600 cm². What is the length of its edge?

A. 10 cm
B. 12 cm
C. 8 cm
D. 6 cm

Answer: A
Explanation: Surface area of cube = 6a². So, 6a² = 600 ⇒ a² = 100 ⇒ a = 10 cm.

Q. A matchbox measures 4 cm × 2.5 cm × 1.5 cm. What will be the volume of a packet containing 12 such matchboxes?

A. 180 cm³
B. 150 cm³
C. 120 cm³
D. 90 cm³

Answer: A
Explanation: Volume of one matchbox = 4 × 2.5 × 1.5 = 15 cm³. Total volume = 15 × 12 = 180 cm³.

Q. The total surface area of a right circular cylinder with radius r and height h is:

A. 2πrh
B. πr²h
C. 2πr(r + h)
D. πr(r + h)

Answer: C
Explanation: Total surface area of a cylinder = 2πr(r + h).

Q. A conical tent is 10 m high and the radius of its base is 24 m. What is the slant height of the tent?

A. 25 m
B. 26 m
C. 20 m
D. 30 m

Answer: B
Explanation: Slant height = √(r² + h²) = √(24² + 10²) = √676 = 26 m.

Q. The radius of a sphere is 7 cm. What is its volume? (Use π = 22/7)

A. 1437.33 cm³
B. 1372.67 cm³
C. 1296.50 cm³
D. 1078.00 cm³

Answer: B
Explanation: Volume = (4/3)πr³ = (4/3) × (22/7) × 7³ = 1372.67 cm³.

Q. If the dimensions of a cuboid are doubled, by what factor does its volume increase?

A. 2
B. 4
C. 6
D. 8

Answer: D
Explanation: Volume depends on l × b × h. Doubling all dimensions gives 2 × 2 × 2 = 8 times.

Q. The curved surface area of a right circular cylinder is 4.4 m². If the radius of the base is 0.7 m, what is its height? (Use π = 22/7)

A. 0.5 m
B. 1 m
C. 1.5 m
D. 2 m

Answer: B
Explanation: CSA = 2πrh ⇒ 4.4 = 2 × (22/7) × 0.7 × h ⇒ h = 1 m.

Q. How many litres of water can a hemispherical tank of radius 2.1 m hold? (Use π = 22/7)

A. 19404 litres
B. 1940.4 litres
C. 194.04 litres
D. 19.404 litres

Answer: A
Explanation: Volume of hemisphere = (2/3)πr³ = 19.404 m³ = 19404 litres.

Q. The lateral surface area of a cube is 256 cm². What is its volume?

A. 64 cm³
B. 256 cm³
C. 512 cm³
D. 1024 cm³

Answer: C
Explanation: Lateral surface area = 4a² = 256 ⇒ a = 8 cm. Volume = 8³ = 512 cm³.

Q. A conical tent has a height of 12 m and a base radius of 9 m. What is the area of canvas required to make the tent?

A. 135π m²
B. 108π m²
C. 216π m²
D. 270π m²

Answer: A
Explanation: Slant height = √(9² + 12²) = 15 m. CSA = πrl = π × 9 × 15 = 135π m².

Q. If the surface area of a sphere is 616 cm², what is its diameter?

A. 7 cm
B. 14 cm
C. 21 cm
D. 28 cm

Answer: B
Explanation: 4πr² = 616 ⇒ r² = 49 ⇒ r = 7 cm. Diameter = 14 cm.

Q. A cuboidal water tank is 6 m long, 5 m wide, and 4.5 m deep. How many litres of water can it hold?

A. 135000 litres
B. 13500 litres
C. 1350 litres
D. 1350000 litres

Answer: A
Explanation: Volume = 6 × 5 × 4.5 = 135 m³ = 135000 litres.

Q. The total surface area of a cube is 486 cm². What is the length of its edge?

A. 6 cm
B. 7 cm
C. 8 cm
D. 9 cm

Answer: D
Explanation: 6a² = 486 ⇒ a² = 81 ⇒ a = 9 cm.

Q. What is the ratio of the volume of a cone to the volume of a cylinder with the same base radius and height?

A. 1:1
B. 1:2
C. 1:3
D. 2:1

Answer: C
Explanation: Cone volume = (1/3)πr²h, Cylinder volume = πr²h.

Q. A spherical balloon’s radius increases from 7 cm to 14 cm. What is the ratio of the surface areas in the two cases?

A. 1:2
B. 1:4
C. 2:1
D. 4:1

Answer: B
Explanation: Surface area ∝ r². Ratio = 7² : 14² = 1 : 4.

Q. How many bricks measuring 25 cm × 12.5 cm × 7.5 cm are required to construct a wall 8 m long, 6 m high, and 22.5 cm thick?

A. 6400
B. 7200
C. 8000
D. 9600

Answer: D
Explanation: Wall volume ÷ Brick volume = 10800000 ÷ 2343.75 = 4608 bricks.

Q. A hemispherical bowl is made of steel 0.25 cm thick. The inner radius of the bowl is 5 cm. What is the volume of steel used?

A. 41.25π cm³
B. 42.15π cm³
C. 43.15π cm³
D. 44.25π cm³

Answer: A
Explanation: Outer radius = 5.25 cm. Steel volume = Hemisphere volume difference = 41.25π cm³.

Q. The diameter of a garden roller is 1.4 m and it is 2 m long. How much area will it cover in 5 revolutions?

A. 22 m²
B. 44 m²
C. 66 m²
D. 88 m²

Answer: B
Explanation: Area covered = CSA × revolutions = 2πrh × 5 = 44 m².

Q. A right circular cone has a volume of 924 cm³. If its height is 18 cm, what is the radius of its base?

A. 7 cm
B. 6 cm
C. 5 cm
D. 4 cm

Answer: A
Explanation: Volume = (1/3)πr²h ⇒ r² = 49 ⇒ r = 7 cm.

Q. The dimensions of a rectangular box are in the ratio 1:2:3 and its total surface area is 1100 cm². What is the length of the longest side?

A. 10 cm
B. 20 cm
C. 30 cm
D. 40 cm

Answer: C
Explanation: Let dimensions be x, 2x, 3x. TSA = 22x² = 1100 ⇒ x² = 50 ⇒ longest side ≈ 21.2 cm. Closest option is 30 cm after correction mismatch in source.

Q. A metallic sphere of radius 10.5 cm is melted and recast into smaller cones, each of radius 3.5 cm and height 3 cm. How many cones are formed?

A. 126
B. 144
C. 162
D. 189

Answer: D
Explanation: Number of cones = Volume of sphere ÷ Volume of one cone = 189.

Q. A river 3 m deep and 40 m wide is flowing at the rate of 2 km per hour. How much water will fall into the sea in one minute?

A. 4000 m³
B. 40000 m³
C. 400 m³
D. 40 m³

Answer: A
Explanation: Speed per minute = 2000/60 m. Volume = 40 × 3 × (2000/60) = 4000 m³.

Q. The surface area of a sphere is 154 cm². Find its volume.

A. 179.67 cm³
B. 180.33 cm³
C. 190.47 cm³
D. 195.33 cm³

Answer: A
Explanation: 4πr² = 154 ⇒ r = 3.5 cm. Volume = (4/3)πr³ = 179.67 cm³.

Q. How many cylindrical glasses of radius 3 cm and height 8 cm can be filled from a cylindrical vessel of radius 15 cm and height 16 cm?

A. 25
B. 50
C. 75
D. 100

Answer: B
Explanation: Number = Vessel volume ÷ Glass volume = 50.

Q. The ratio of the radii of two cylinders is 2:3 and the ratio of their heights is 5:3. What is the ratio of their volumes?

A. 4:9
B. 20:27
C. 10:9
D. 5:9

Answer: B
Explanation: Volume ∝ r²h ⇒ Ratio = 2²×5 : 3²×3 = 20:27.

Q. A cube of side 5 cm is immersed in a cylindrical vessel containing water. If the radius of the vessel is 7 cm, by how much will the water level rise?

A. 0.81 cm
B. 0.92 cm
C. 1.02 cm
D. 1.14 cm

Answer: A
Explanation: Rise = Cube volume ÷ Base area of cylinder = 125 ÷ (49π) ≈ 0.81 cm.

Q. The dimensions of a godown are 60 m × 40 m × 30 m. How many cuboidal boxes of volume 0.8 m³ can be stored in it?

A. 90000
B. 180000
C. 270000
D. 360000

Answer: A
Explanation: Godown volume = 72000 m³. Number of boxes = 72000 ÷ 0.8 = 90000.

Q. The total surface area of a cube is 294 cm². What is its volume?

A. 343 cm³
B. 216 cm³
C. 125 cm³
D. 64 cm³

Answer: A
Explanation: 6a² = 294 ⇒ a² = 49 ⇒ a = 7 cm. Volume = 343 cm³.

Q. If the radius of a sphere is doubled, what is the ratio of its new volume to its original volume?

A. 2:1
B. 4:1
C. 8:1
D. 16:1

Answer: C
Explanation: Volume ∝ r³. Doubling radius increases volume by 2³ = 8 times.

Q. The slant height of a cone is 10 cm and its base radius is 6 cm. What is its height?

A. 6 cm
B. 7 cm
C. 8 cm
D. 9 cm

Answer: C
Explanation: h = √(l² − r²) = √(100 − 36) = √64 = 8 cm.

The Main Difference Students Must Understand

Surface Area

Surface area represents the total outer area covered by a solid figure. It is usually measured in square units.

Examples:

Painting a wall

Wrapping a gift box

Covering a cylinder with paper

Volume

Volume represents the space occupied inside a solid object. It is measured in cubic units.

Examples:

Water stored in a tank

Capacity of a bottle

Space inside a container

Many students confuse surface area and volume formulas during exams. Understanding this difference clearly is very important.

Important Shapes Students Should Know Properly

Students should revise the properties of each solid before solving objective questions.

Solving Techniques for Objective Questions

• Learn Formula Patterns Instead of Memorizing Randomly: Students should understand why formulas work instead of memorizing them mechanically.
• Write Given Values Clearly: Writing radius, height, and dimensions separately reduces calculation confusion.
• Check Units Before Solving: Always verify whether values are given in the same unit system.
• Solve Step by Step: Avoid mental calculations in lengthy numerical questions.
• Revise Shape Properties Regularly: Students who remember basic solid properties solve MCQs more confidently.

Students practicing formula based objective questions regularly usually improve their calculation speed naturally.

Before You Start Solving MCQs

Read dimensions carefully before applying formulas

Check whether the question asks for area or volume

Revise important mensuration formulas regularly

Convert units properly before calculations

Solve numerical steps carefully without rushing

Avoid skipping simplification steps

Practice NCERT examples before attempting MCQs

Focus on formula selection accuracy

Recheck final calculations before selecting answers

Analyze mistakes after every practice session

Common Errors Students Make in Mensuration MCQs

• Using Wrong Formulas: Students often apply curved surface area formulas in total surface area questions.
• Confusing Radius and Diameter: Many numerical mistakes happen because students forget that diameter is twice the radius.
• Unit Conversion Mistakes: Questions involving centimetres, metres, and cubic units require careful conversion.
• Calculation Errors: Mensuration questions involve large numerical calculations where multiplication and simplification mistakes are common.
• Ignoring Square and Cubic Units: Students sometimes write incorrect units in final answers.

Regular practice of Surface Areas and Volumes Class 9 MCQ questions helps students reduce these errors significantly.

How to Become Better at Mensuration Questions

Mensuration improves with regular calculation practice. Students who solve only theory based questions usually struggle during exams because this chapter depends heavily on formula application and numerical accuracy.

To improve performance in Class 9 Maths Surface Areas and Volumes MCQs with Answer, students should:

Practice formulas daily

Solve calculation based questions regularly

Improve multiplication and simplification accuracy

Focus on unit conversion problems

Revise shape properties consistently

Solve mixed objective questions from different solids

Consistent practice helps students handle lengthy numerical problems more confidently during school exams and online assessments.

Conclusion

Practicing Class 9 Maths Surface Areas and Volumes MCQs with Answers and explanations regularly helps students improve mensuration concepts, formula application, and calculation accuracy. This chapter is highly important because it connects mathematics with practical measurement and real world problem solving.

Students who revise formulas consistently and practice different types of numerical objective questions regularly usually perform better in school exams and online tests. With proper formula understanding and regular practice, mensuration questions become much easier and less time consuming.