V=πr²h l V=πr²h/3 V=4πr³/3 TSA=3πr² Cube: SA=6a², V=a³ l=√(r²+h²) for cone
V=πr²h
Chapter 11  ·  Class IX Mathematics  ·  MCQ Practice

MCQ Practice Arena

Surface Areas and Volumes

Cuboid to Sphere — Build Your Formula Table and Dominate Every 3D Problem

📋 50 MCQs ⭐ 26 PYQs ⏱ 70 sec/Q
🚀 Start Practising 📖 Revise Notes First

MCQ Bank Snapshot

50Total MCQs
18Easy
22Medium
10Hard
26PYQs
70 secAvg Time/Q
7Topics
Easy 36% Medium 44% Hard 20%

Why Practise These MCQs?

CBSE Class IXState BoardsNTSE

Surface Areas and Volumes in Class IX introduces 3D mensuration — cuboid, cube, cylinder, cone, sphere, and hemisphere. CBSE awards 8–10 marks from this chapter; MCQs test single-solid formulae while long-answer questions test combinations. NTSE includes unit conversion and volume comparison problems. Unlike Class X which has frustum, Class IX focuses on the six core solids — create a formula table and these MCQs become mechanical.

Topic-wise MCQ Breakdown

Cuboid — SA & Volume8 Q
Cube — SA & Volume6 Q
Right Circular Cylinder — SA & Volume10 Q
Right Circular Cone — SA & Volume10 Q
Sphere — SA & Volume8 Q
Hemisphere — SA & Volume5 Q
Unit Conversions & Real-Life Problems3 Q

Must-Know Formulae Before You Start

Recall these cold before attempting MCQs — they appear in >70% of questions.

$\text{Cuboid: LSA}=2(l+b)h,\ TSA=2(lb+bh+lh),\ V=lbh$
$\text{Cube: SA}=6a^2,\ V=a^3$
$\text{Cylinder: CSA}=2\pi rh,\ TSA=2\pi r(r+h),\ V=\pi r^2 h$
$\text{Cone: CSA}=\pi rl,\ TSA=\pi r(l+r),\ V=\tfrac{1}{3}\pi r^2 h,\ l=\sqrt{r^2+h^2}$
$\text{Sphere: SA}=4\pi r^2,\ V=\tfrac{4}{3}\pi r^3$
$\text{Hemisphere: CSA}=2\pi r^2,\ TSA=3\pi r^2,\ V=\tfrac{2}{3}\pi r^3$

MCQ Solving Strategy

Create a 6-row formula table (one row per solid) with columns: Solid | CSA/LSA | TSA | Volume | Special. Memorise this table — it covers every MCQ. For cone MCQs, always compute slant height l = √(r²+h²) first if it is not given. For cylinder problems, identify whether the question asks for CSA (just the curved surface, no caps) or TSA (including both circular ends). Use π = 22/7 when r is a multiple of 7.

⚠ Common Traps & Errors

Difficulty Ladder

Work through each rung in order — do not jump to Hard before mastering Easy.

① Easy

Single-formula MCQs: cube, cuboid SA and volume

② Medium

Cylinder, cone, sphere formulae; find r or h given SA or V

③ Hard

Hemisphere, slant height computation, combined/hollow solid problems

★ PYQ

CBSE — cone + cylinder + sphere; NTSE — volume comparison and conversion

Continue Your Preparation

📖 Chapter Notes Revise concepts & theory 🧠 MCQ Practice Topic-wise Questions 📘✔️ Exercises Step-by-step NCERT solutions ✔️❌ True / False Concept-based True & False ➡ Next Chapter Statistics
🎯 Knowledge Check

Maths — SURFACE AREAS AND VOLUMES

50 Questions Class 9 MCQs
1
The curved surface area of a cylinder is given by
2
Total surface area of a cuboid is
3
Volume of a cube with side \(‘a’\) is
4
A solid cone has radius r and height \(h\). Its volume is
5
The curved surface area of a cone is
6
Total surface area of a hemisphere (including base) is
7
Volume of a sphere of radius \(r\)
8
The CSA of a cylinder is independent of
9
If the diameter of hemisphere is 14 cm, its radius is
10
TSA of a cube of side a
11
Volume of a cuboid is
12
Slant height of cone is
13
The CSA of a hemisphere is
14
The area of the base of a cylinder is
15
TSA of a right circular cylinder
16
A cube has 12 edges; the total length of edges is
17
A cuboid has how many faces?
18
A solid with circular base and one vertex
19
Units of surface area
20
Units of volume
21
A sphere has
22
CSA of hollow cylinder depends on
23
\(1 m^3 =\)
24
TSA of sphere is
25
The CSA of a cone depends on
26
A cube has how many vertices?
27
A cube has how many faces?
28
Volume of hollow cylinder
29
Area of curved surface of sphere is same as
30
Rainwater harvesting tank shape is commonly
31
A hemisphere has how many faces?
32
Total surface area of hemisphere includes
33
If cube side becomes double, its volume becomes
34
Surface area of cube becomes how many times if side is doubled?
35
Cross section of cylinder is
36
A cone and cylinder have same base radius and height. Who has greater volume?
37
A hemisphere is half of
38
The slant height of cone increases if
39
Area of circle formula
40
The shape with maximum volume for given surface area
41
A sphere has how many faces?
42
If radius of sphere doubles, TSA becomes
43
If radius of sphere doubles, volume becomes
44
Cylinder has how many edges?
45
A hemisphere has how many edges?
46
Cone has how many edges?
47
Shape of ice cream cone top
48
In cylinder, height is
49
Slant height is always
50
CSA of frustum of cone is
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NCERT Class 9 Maths Chapter 11 Surface Areas & Volumes MCQs
NCERT Class 9 Maths Chapter 11 Surface Areas & Volumes MCQs — Complete Notes & Solutions · academia-aeternum.com
Surface Areas and Volumes introduces Class IX learners to the real-world application of geometry through the study of 3D shapes, their surface areas, and volumes. Students explore cubes, cuboids, cylinders, cones, spheres, and hemispheres using simple formulas derived from practical reasoning. These concepts build strong spatial understanding and are crucial for competitive exams, school tests, Olympiads, and higher classes. With a clear focus on NCERT content, this chapter helps students…
🎓 Class 9 📐 Mathematics 📖 NCERT ✅ Free Access 🏆 CBSE · JEE
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    ACADEMIA AETERNUM तमसो मा ज्योतिर्गमय · Est. 2025
    Sharing this chapter
    NCERT Class 9 Maths Chapter 11 Surface Areas & Volumes MCQs
    NCERT Class 9 Maths Chapter 11 Surface Areas & Volumes MCQs — Complete Notes & Solutions · academia-aeternum.com
    Surface Areas and Volumes introduces Class IX learners to the real-world application of geometry through the study of 3D shapes, their surface areas, and volumes. Students explore cubes, cuboids, cylinders, cones, spheres, and hemispheres using simple formulas derived from practical reasoning. These concepts build strong spatial understanding and are crucial for competitive exams, school tests, Olympiads, and higher classes. With a clear focus on NCERT content, this chapter helps students…
    🎓 Class 9 📐 Mathematics 📖 NCERT ✅ Free Access 🏆 CBSE · JEE
    Share on
    WhatsApp
    Telegram
    X / Twitter
    Facebook
    Instagram
    Threads
    Pinterest
    LinkedIn
    Quora
    Discord
    Reddit
    Email
    academia-aeternum.com/class-9/mathematics/surface-areas-and-volumes/mcqs/ Copy link
    💡
    Exam tip: Sharing chapter notes with your study group creates a reinforcement loop. Teaching a concept is the fastest path to mastering it.

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