Chapter 12 · Class X Mathematics · MCQ Practice

MCQ Practice Arena

Surface Areas & Volumes

Eighteen Formulae, One Strategy — Build Your Formula Table and Dominate

📋 50 MCQs ⭐ 28 PYQs ⏱ 75 sec/Q

🚀 Start Practising 📖 Revise Notes First

MCQ Bank Snapshot

50Total MCQs

16Easy

22Medium

12Hard

28PYQs

75 secAvg Time/Q

8Topics

Easy 32% Medium 44% Hard 24%

Why Practise These MCQs?

CBSE Class XState BoardsNTSE

Surface Areas & Volumes is the highest-formula-count chapter in Class X — memorising 18+ formulae is non-negotiable. CBSE Boards assign 10–12 marks; combination solid problems (cone + hemisphere, cylinder + sphere) and conversion problems (melting one shape into another) are the standard 4–5 mark types. MCQ practice here builds formula recall speed. NTSE tests all standard formulas directly.

Topic-wise MCQ Breakdown

Cuboid SA & Volume4 Q

Cylinder SA & Volume8 Q

Cone SA & Volume10 Q

Sphere & Hemisphere SA & Volume10 Q

Frustum of Cone6 Q

Combinations of Solids (SA)5 Q

Conversion Problems (Volume preserved)5 Q

Hollow Shapes & Material Volume2 Q

Must-Know Formulae Before You Start

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

$\text{Cylinder: }CSA=2\pi rh,\ V=\pi r^2h$

$\text{Cone: }CSA=\pi rl,\ V=\tfrac{1}{3}\pi r^2h,\ l=\sqrt{r^2+h^2}$

$\text{Sphere: }SA=4\pi r^2,\ V=\tfrac{4}{3}\pi r^3$

$\text{Hemisphere: }CSA=2\pi r^2,\ TSA=3\pi r^2,\ V=\tfrac{2}{3}\pi r^3$

$\text{Frustum: }V=\tfrac{\pi h}{3}(R^2+r^2+Rr)$

$\text{Frustum slant: }l=\sqrt{h^2+(R-r)^2}$

MCQ Solving Strategy

Create a formula table on paper before solving — 18 formulae with CSA, TSA, and V for each solid. For combination solid MCQs, identify: which surfaces are VISIBLE (outer surface only — not where shapes join). For conversion MCQs: Volume₁ = Volume₂ (conservation of material). Frustum is the hardest — practice finding slant height l = √(h²+(R−r)²) before using any other formula.

⚠ Common Traps & Errors

⚠Cone TSA = πrl + πr² (base) — don't forget the base
⚠Hemisphere TSA = 3πr² (curved + flat base), CSA = 2πr² (curved only)
⚠Combination solids: subtract the joined base from total SA
⚠Conversion: equate VOLUMES, not surface areas
⚠Frustum: R is the larger radius, r is the smaller radius

Difficulty Ladder

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

① Easy

Single solid SA and V for cylinder, cone, sphere

② Medium

Hemisphere, frustum, find dimension given SA or V

③ Hard

Combination solids, conversion problems, hollow shapes

★ PYQ

CBSE — combination + conversion; NTSE — direct formula application

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 10 MCQs

What is the total surface area of a cube of edge $a$?

a a. $3a^2$ b b. $4a^2$ c c. $6a^2$ d d. $a^3$

The volume of a cube of side $a$ is:

a a. $6a^2$ b b. $3a^2$ c c. $a^2$ d d. $a^3$

What is the curved surface area of a right circular cylinder of radius $r$ and height $h$?

a a. $\pi r^2$ b b. $2\pi rh$ c c. $\pi r^2 h$ d d. $2\pi r(r+h)$

The total surface area of a cuboid with dimensions $l, b, h$ is:

a a. $lb + bh + hl$ b b. $2(lb + bh + hl)$ c c. $lbh$ d d. $4(lb + bh + hl)$

The volume of a right circular cylinder is:

a a. $2\pi rh$ b b. $\pi r^2$ c c. $\pi r^2 h$ d d. $\frac{1}{3}\pi r^2 h$

What is the curved surface area of a cone?

a a. $\pi r^2$ b b. $\pi rl$ c c. $2\pi rl$ d d. $\frac{1}{3}\pi r^2 h$

The slant height $l$ of a cone is given by:

a a. $l = r + h$ b b. $l = \sqrt{r^2 - h^2}$ c c. $l = \sqrt{r^2 + h^2}$ d d. $l = \frac{r^2}{h}$

The volume of a cone is:

a a. $\pi r^2 h$ b b. $\frac{1}{2}\pi r^2 h$ c c. $\frac{1}{3}\pi r^2 h$ d d. $2\pi r^2 h$

The surface area of a sphere of radius $r$ is:

a a. $2\pi r^2$ b b. $3\pi r^2$ c c. $4\pi r^2$ d d. $\frac{4}{3}\pi r^3$

The volume of a sphere is:

a a. $4\pi r^2$ b b. $\frac{4}{3}\pi r^3$ c c. $3\pi r^3$ d d. $\pi r^3$

The curved surface area of a hemisphere is:

a a. $\pi r^2$ b b. $2\pi r^2$ c c. $3\pi r^2$ d d. $4\pi r^2$

The total surface area of a hemisphere is:

a a. $2\pi r^2$ b b. $3\pi r^2$ c c. $4\pi r^2$ d d. $\pi r^2$

The volume of a hemisphere is:

a a. $\frac{2}{3}\pi r^3$ b b. $\pi r^3$ c c. $\frac{4}{3}\pi r^3$ d d. $2\pi r^3$

If the radius of a sphere is doubled, its volume becomes:

a a. double b b. triple c c. four times d d. eight times

If the height of a cylinder is doubled, its volume:

a a. remains same b b. becomes double c c. becomes four times d d. becomes half

Which quantity remains constant when a solid is melted and recast?

a a. Surface area b b. Height c c. Volume d d. Shape

A hollow cylinder differs from a solid cylinder because it has:

a a. greater height b b. thickness c c. no volume d d. no surface area

The volume of a hollow cylinder is given by:

a a. $\pi h(R^2 + r^2)$ b b. $\pi h(R^2 - r^2)$ c c. $2\pi h(R + r)$ d d. $2\pi h(R - r)$

Painting the outside of a solid involves calculation of:

a a. volume b b. capacity c c. surface area d d. density

Capacity of a container is measured by:

a a. surface area b b. volume c c. perimeter d d. height

The unit of volume in SI system is:

a a. $\text{cm}^2$ b b. $\text{m}^2$ c c. $\text{cm}^3$ d d. $\text{m}^3$

The unit of surface area is:

a a. cubic unit b b. square unit c c. linear unit d d. litre

A solid formed by combining a cone and a hemisphere will have volume equal to:

a a. difference of volumes b b. product of volumes c c. sum of volumes d d. average of volumes

Which formula uses slant height?

a a. Volume of cone b b. CSA of cone c c. Volume of cylinder d d. TSA of sphere

If all dimensions of a solid are halved, its volume becomes:

a a. half b b. one-fourth c c. one-eighth d d. double

A sphere has the same volume as a cone. The relationship involves:

a a. equal radii only b b. equal heights only c c. volume comparison d d. equal surface areas

Which solid has no flat surface?

a a. Cone b b. Cylinder c c. Sphere d d. Hemisphere

The base of a cone is:

a a. square b b. triangle c c. rectangle d d. circle

A cuboid has how many faces?

a a. 4 b b. 5 c c. 6 d d. 8

The curved surface area of a sphere is:

a a. $\pi r^2$ b b. $2\pi r^2$ c c. $3\pi r^2$ d d. $4\pi r^2$

Which solid has both curved and flat surfaces?

a a. Sphere b b. Cube c c. Cylinder d d. Cuboid

If the radius of a cylinder is tripled, its volume becomes:

a a. 3 times b b. 6 times c c. 9 times d d. 27 times

Which solid has exactly one curved surface and one flat surface?

a a. Sphere b b. Hemisphere c c. Cube d d. Cuboid

When converting cm into m, we divide by:

a a. 10 b b. 100 c c. 1000 d d. 10000

Which chapter concept is used in water tank problems?

a a. Coordinate geometry b b. Trigonometry c c. Surface areas and volumes d d. Statistics

The shape of an ice-cream cone is:

a a. cylinder b b. hemisphere c c. cone d d. sphere

The formula $2\pi r(h+r)$ represents:

a a. CSA of cylinder b b. TSA of cylinder c c. Volume of cylinder d d. CSA of cone

A metallic sphere is melted and recast into a cube. Which remains same?

a a. Surface area b b. Edge length c c. Volume d d. Shape

Which solid has the maximum volume for the same surface area?

a a. Cube b b. Cuboid c c. Sphere d d. Cylinder

The base area of a cylinder is:

a a. $2\pi r$ b b. $\pi r^2$ c c. $2\pi rh$ d d. $r^2$

A cone and a cylinder have equal base and height. The ratio of their volumes is:

a a. 1:1 b b. 1:2 c c. 1:3 d d. 3:1

Which solid is used to model a football?

a a. Cube b b. Cylinder c c. Sphere d d. Cone

The surface area of a cuboid depends on:

a a. only length b b. only breadth c c. only height d d. length, breadth and height

What does mensuration mainly deal with?

a a. Shapes and angles b b. Measurement of figures c c. Data analysis d d. Equations

A solid with equal length, breadth and height is:

a a. cuboid b b. cone c c. cylinder d d. cube

Which quantity increases faster with increase in dimensions?

a a. Length b b. Area c c. Volume d d. Perimeter

The diameter of a sphere is:

a a. $r$ b b. $2r$ c c. $3r$ d d. $\frac{r}{2}$

A tent is generally shaped like a:

a a. cube b b. cuboid c c. cone d d. sphere

Which solid has two circular faces?

a a. Cone b b. Sphere c c. Cylinder d d. Hemisphere

Surface Areas and Volumes mainly helps in:

a a. abstract algebra b b. practical measurements c c. graph plotting d d. probability

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Multiple Choice Questions play a vital role in strengthening conceptual clarity and exam readiness for the chapter Surface Areas and Volumes. This chapter demands precision in formula application, strong visualisation of three-dimensional solids, and the ability to interpret real-life situations mathematically. MCQs test not only memory of formulae but also analytical thinking, dimensional reasoning, and the correct identification of solids involved in a problem. The following MCQs are…

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Surface Areas & Volumes

MCQ Bank Snapshot

Why Practise These MCQs?

Topic-wise MCQ Breakdown

Must-Know Formulae Before You Start

MCQ Solving Strategy

⚠ Common Traps & Errors

Difficulty Ladder

Continue Your Preparation

Maths — SURFACE AREAS AND VOLUMES

Frequently Asked Questions

Recent Posts

SURFACE AREAS AND VOLUMES — Learning Resources

Let's Connect

Surface Areas & Volumes

MCQ Bank Snapshot

Why Practise These MCQs?

Topic-wise MCQ Breakdown

Must-Know Formulae Before You Start

MCQ Solving Strategy

⚠ Common Traps & Errors

Difficulty Ladder

Continue Your Preparation

Maths — SURFACE AREAS AND VOLUMES

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