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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Frequently Asked Questions

The surface area of a solid is the total area covered by all its outer faces. It represents the amount of material required to cover the solid from the outside.

Volume is the measure of space occupied by a solid object. It indicates the capacity of the solid to hold material such as liquid or gas.

Curved surface area is the area of only the curved part of a solid, excluding any flat circular or polygonal faces.

Total surface area is the sum of the curved surface area and the areas of all flat faces of a solid.

The chapter includes cube, cuboid, right circular cylinder, right circular cone, sphere, hemisphere, hollow solids, and combinations of these solids.

The total surface area of a cube is given by $6a^2$, where $a$ is the length of one edge.

The volume of a cuboid is calculated using the formula $l \times b \times h$, where $l$, $b$, and $h$ are length, breadth, and height respectively.

The curved surface area of a cylinder is $2\pi rh$, where $r$ is the radius and $h$ is the height.

The total surface area of a cylinder is $2\pi r(h + r)$, which includes the curved surface and both circular ends.

Slant height is the distance from the centre of the base of a cone to a point on the curved surface along the side. It is denoted by $l$.

Slant height is calculated using $l = \sqrt{r^2 + h^2}$, where $r$ is radius and $h$ is height of the cone.

The volume of a cone is $\frac{1}{3}\pi r^2 h$.

The surface area of a sphere is $4\pi r^2$, where $r$ is the radius.

The volume of a sphere is $\frac{4}{3}\pi r^3$.

A hemisphere is exactly half of a sphere, having one flat circular face and one curved surface.

SURFACE AREAS AND VOLUMES – Learning Resources

Detailed Notes

True / False

NCERT Solutions

ACADEMIA AETERNUM तमसो मा ज्योतिर्गमय · Est. 2025

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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

Q 01 What is meant by surface area of a solid?

Q 02 What is volume of a solid?

Q 03 What is curved surface area \(CSA\)?

Q 04 What is total surface area \(TSA\)?

Q 05 What are the basic solids studied in this chapter?

Q 06 What is the formula for the surface area of a cube?

Q 07 How is the volume of a cuboid calculated?

Q 08 What is the curved surface area of a cylinder?

Q 09 How do you find the total surface area of a cylinder?

Q 10 What is slant height in a cone?

Q 11 How is slant height of a cone calculated?

Q 12 What is the formula for volume of a cone?

Q 13 What is the surface area of a sphere?

Q 14 How is volume of a sphere calculated?

Q 15 What is the difference between a sphere and a hemisphere?

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SURFACE AREAS AND VOLUMES – Learning Resources

Detailed Notes

True / False

NCERT Solutions

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