Understanding three-dimensional figures becomes much more practical when students start calculating outer surfaces, capacities, and measurements of real objects mathematically, and that is exactly what students learn in Surface Areas and Volumes. This chapter mainly focuses on solid shapes such as cones, cylinders, spheres, hemispheres, and frustums, along with their surface areas and volume calculations. Practicing Surface Areas and Volumes Class 10 MCQs regularly helps students improve mensuration understanding, formula application, and geometry calculation skills for CBSE board exams. The latest CBSE pattern now focuses more on competency-based and application-oriented learning, where students must understand practical shape measurements instead of depending only on direct formula memorization. Regular practice of Surface Areas and Volumes Class 10 MCQs with Answers helps students improve calculation speed, figure interpretation, and logical problem-solving confidence naturally. Students preparing for board examinations can also explore MCQs, Class 10 MCQs, CBSE Board, and MCQs Class 10 Maths for chapter-wise objective practice based on the latest syllabus and board exam trends.
Why Surface Areas and Volumes is Important in Class 10 Maths
Surface Areas and Volumes is one of the most practical mensuration chapters because it explains how real-life objects are measured mathematically using geometry formulas.
This chapter helps students understand:
outer covering measurements,
storage capacities,
curved surfaces,
and three-dimensional geometry relationships.
This chapter is important because:
Surface Areas and Volumes Class 10 MCQs are frequently asked in CBSE board exams
Formula application skills improve significantly
Students learn practical shape measurements
3D geometry understanding becomes stronger
Competency-based questions are increasing
Visualization skills improve naturally
Capacity and surface calculations become easier
Students who practice Surface Areas and Volumes MCQs Class 10 regularly usually solve mensuration questions more confidently in exams.
Important Concepts Covered in Surface Areas and Volumes Class 10 MCQs
Before solving Surface Areas and Volumes Class 10 MCQs with Answers, students should revise all important formulas and concepts carefully because most objective questions are directly formula and figure based.
Important concepts covered in this chapter include:
- Cone
- Cylinder
- Sphere
- Hemisphere
- Frustum of cone
- Curved surface area
- Total surface area
- Volume calculations
- Radius and diameter relationships
- Height and slant height
- Capacity measurements
- Solid figure combinations
These concepts are very important for solving CBSE Surface Areas and Volumes Class 10 MCQs accurately.
Surface Areas and Volumes Class 10 MCQs with Answers
Practice important and exam-oriented Surface Areas and Volumes Class 10 MCQs designed according to the latest CBSE pattern and competency-based learning approach. These objective questions help students improve formula understanding, mensuration calculations, 3D figure analysis, and board exam preparation skills effectively.
Q. A cone has radius 6 cm and height 8 cm. Find its slant height.
A) 8 cm
B) 9 cm
C) 10 cm
D) 12 cm
Answer: C
Explanation:
Slant height = sqrt(r^2 + h^2)
= sqrt(6^2 + 8^2)
= sqrt(36 + 64)
= sqrt(100) = 10 cm.
Q. Find the curved surface area of a cylinder having radius 7 cm and height 15 cm.
A) 550 sq cm
B) 660 sq cm
C) 770 sq cm
D) 880 sq cm
Answer: B
Explanation:
Curved surface area = 2pi rh
= 2 x (22/7) x 7 x 15
= 660 sq cm.
Q. The volume of a cube with side 11 cm is:
A) 121 cubic cm
B) 726 cubic cm
C) 1331 cubic cm
D) 1452 cubic cm
Answer: C
Explanation:
Volume of cube = side^3
= 11^3 = 1331 cubic cm.
Q. A sphere has radius 14 cm. Find its volume.
A) 11494.67 cubic cm
B) 11500 cubic cm
C) 12000 cubic cm
D) 11088 cubic cm
Answer: A
Explanation:
Volume of sphere = (4/3)pi r^3
= (4/3) x (22/7) x 14 x 14 x 14
≈ 11494.67 cubic cm.
Q. Find the total surface area of a hemisphere of radius 7 cm.
A) 308 sq cm
B) 462 sq cm
C) 616 sq cm
D) 154 sq cm
Answer: B
Explanation:
Total surface area of hemisphere = 3pi r^2
= 3 x (22/7) x 7 x 7
= 462 sq cm.
Q. The curved surface area of a cone with radius 5 cm and slant height 12 cm is:
A) 60pi sq cm
B) 50pi sq cm
C) 70pi sq cm
D) 80pi sq cm
Answer: A
Explanation:
CSA of cone = pi r l
= pi x 5 x 12
= 60pi sq cm.
Q. A cuboid has dimensions 15 cm x 8 cm x 6 cm. Find its volume.
A) 620 cubic cm
B) 720 cubic cm
C) 840 cubic cm
D) 900 cubic cm
Answer: B
Explanation:
Volume = l x b x h
= 15 x 8 x 6
= 720 cubic cm.
Q. The radius of a sphere is doubled. Its surface area becomes:
A) 2 times
B) 3 times
C) 4 times
D) 8 times
Answer: C
Explanation:
Surface area depends on r^2.
If radius doubles, area becomes 2^2 = 4 times.
Q. Find the volume of a cylinder with radius 4 cm and height 21 cm.
A) 336pi cubic cm
B) 420pi cubic cm
C) 252pi cubic cm
D) 168pi cubic cm
Answer: A
Explanation:
Volume = pi r^2 h
= pi x 4^2 x 21
= 336pi cubic cm.
Q. A cone has height 24 cm and radius 7 cm. Find its slant height.
A) 24 cm
B) 25 cm
C) 26 cm
D) 27 cm
Answer: B
Explanation:
l = sqrt(h^2 + r^2)
= sqrt(24^2 + 7^2)
= sqrt(576 + 49)
= sqrt(625) = 25 cm.
Q. The total surface area of a cube with side 9 cm is:
A) 324 sq cm
B) 486 sq cm
C) 576 sq cm
D) 729 sq cm
Answer: B
Explanation:
TSA of cube = 6a^2
= 6 x 9^2
= 6 x 81
= 486 sq cm.
Q. Find the curved surface area of a hemisphere of radius 14 cm.
A) 1232 sq cm
B) 616 sq cm
C) 2464 sq cm
D) 1848 sq cm
Answer: A
Explanation:
CSA of hemisphere = 2pi r^2
= 2 x (22/7) x 14 x 14
= 1232 sq cm.
Q. A cone and cylinder have the same base radius and height. Find the ratio of their volumes.
A) 1:2
B) 1:3
C) 2:3
D) 3:1
Answer: B
Explanation:
Volume of cone = (1/3)pi r^2 h
Volume of cylinder = pi r^2 h
Ratio = 1:3.
Q. Find the total surface area of a cylinder with radius 3.5 cm and height 10 cm.
A) 231 sq cm
B) 275 sq cm
C) 300 sq cm
D) 350 sq cm
Answer: A
Explanation:
TSA = 2pi r(r + h)
= 2 x (22/7) x 3.5 x (3.5 + 10)
= 231 sq cm.
Q. The volume of a hemisphere of radius 6 cm is:
A) 144pi cubic cm
B) 288pi cubic cm
C) 72pi cubic cm
D) 216pi cubic cm
Answer: A
Explanation:
Volume of hemisphere = (2/3)pi r^3
= (2/3)pi x 6^3
= 144pi cubic cm.
Q. A sphere has diameter 18 cm. Find its surface area.
A) 972pi sq cm
B) 648pi sq cm
C) 324pi sq cm
D) 486pi sq cm
Answer: C
Explanation:
Radius = 18/2 = 9 cm
Surface area = 4pi r^2
= 4pi x 9^2
= 324pi sq cm.
Q. Find the height of a cone whose slant height is 13 cm and radius is 5 cm.
A) 10 cm
B) 11 cm
C) 12 cm
D) 14 cm
Answer: C
Explanation:
h = sqrt(l^2 - r^2)
= sqrt(13^2 - 5^2)
= sqrt(169 - 25)
= sqrt(144) = 12 cm.
Q. The radius of a cylinder is 7 cm and height is 20 cm. Find its volume.
A) 3080 cubic cm
B) 2800 cubic cm
C) 3200 cubic cm
D) 2500 cubic cm
Answer: A
Explanation:
Volume = pi r^2 h
= (22/7) x 7 x 7 x 20
= 3080 cubic cm.
Q. Find the volume of a cone with radius 6 cm and height 14 cm.
A) 168pi cubic cm
B) 196pi cubic cm
C) 210pi cubic cm
D) 252pi cubic cm
Answer: A
Explanation:
Volume = (1/3)pi r^2 h
= (1/3)pi x 6^2 x 14
= 168pi cubic cm.
Q. The total surface area of a sphere of radius 7 cm is:
A) 616 sq cm
B) 462 sq cm
C) 308 sq cm
D) 154 sq cm
Answer: A
Explanation:
Surface area = 4pi r^2
= 4 x (22/7) x 7 x 7
= 616 sq cm.
Q. A metallic cube of side 6 cm is melted to form small cubes of side 2 cm. Find the number of small cubes formed.
A) 9
B) 18
C) 27
D) 36
Answer: C
Explanation:
Number of cubes = (6^3)/(2^3)
= 216/8
= 27.
Q. Find the curved surface area of a cone with radius 14 cm and slant height 20 cm.
A) 280pi sq cm
B) 300pi sq cm
C) 240pi sq cm
D) 350pi sq cm
Answer: A
Explanation:
CSA = pi r l
= pi x 14 x 20
= 280pi sq cm.
Q. A cuboid has dimensions 18 cm x 10 cm x 5 cm. Find its total surface area.
A) 640 sq cm
B) 720 sq cm
C) 560 sq cm
D) 460 sq cm
Answer: C
Explanation:
TSA = 2(lb + bh + hl)
= 2(18x10 + 10x5 + 18x5)
= 2(180 + 50 + 90)
= 640 sq cm.
Q. Find the radius of a sphere whose volume is 288pi cubic cm.
A) 4 cm
B) 5 cm
C) 6 cm
D) 7 cm
Answer: C
Explanation:
(4/3)pi r^3 = 288pi
r^3 = 216
r = 6 cm.
Q. The slant height of a cone is 15 cm and radius is 9 cm. Find its height.
A) 10 cm
B) 11 cm
C) 12 cm
D) 13 cm
Answer: C
Explanation:
Height = sqrt(15^2 - 9^2)
= sqrt(225 - 81)
= sqrt(144) = 12 cm.
Q. A cylinder has radius 5 cm and height 18 cm. Find its curved surface area.
A) 540pi sq cm
B) 180pi sq cm
C) 90pi sq cm
D) 360pi sq cm
Answer: B
Explanation:
CSA = 2pi rh
= 2pi x 5 x 18
= 180pi sq cm.
Q. A sphere of radius 12 cm is melted into spheres of radius 3 cm. Find the number of small spheres formed.
A) 16
B) 32
C) 64
D) 128
Answer: C
Explanation:
Number of spheres = (12^3)/(3^3)
= 1728/27
= 64.
Q. Find the total surface area of a cone with radius 7 cm and slant height 24 cm.
A) 217pi sq cm
B) 224pi sq cm
C) 231pi sq cm
D) 248pi sq cm
Answer: A
Explanation:
TSA = pi r(r + l)
= pi x 7 x (7 + 24)
= 217pi sq cm.
Q. The volume of a sphere is 1372/3 pi cubic cm. Find its radius.
A) 5 cm
B) 6 cm
C) 7 cm
D) 8 cm
Answer: C
Explanation:
(4/3)pi r^3 = (1372/3)pi
4r^3 = 1372
r^3 = 343
r = 7 cm.
Q. Find the total surface area of a cuboid having dimensions 12 cm x 9 cm x 5 cm.
A) 426 sq cm
B) 438 sq cm
C) 456 sq cm
D) 468 sq cm
Answer: A
Explanation:
TSA = 2(lb + bh + hl)
= 2(12x9 + 9x5 + 12x5)
= 2(108 + 45 + 60)
= 426 sq cm.
Instructions Before Solving Surface Areas and Volumes MCQs
- Read all dimensions carefully before applying formulas because mensuration questions often contain multiple measurements together.
- Check whether the question uses radius or diameter because students frequently confuse both values.
- Identify whether the question asks for CSA, TSA, or volume before starting calculations.
- Use the correct formula according to the shape because similar-looking figures may require different formulas.
- Convert units properly whenever necessary because unit conversion mistakes are common in mensuration questions.
- Apply formulas step-by-step instead of solving mentally because volume calculations require careful substitution.
- Observe combined solid figures carefully because many competency-based questions involve multiple shapes together.
- Practice application-oriented and competency-based Surface Areas and Volumes Class 10 MCQs regularly because the latest CBSE pattern focuses heavily on conceptual understanding.
Common Mistakes Students Make in Surface Areas and Volumes Questions
Many students lose marks in Surface Areas and Volumes Class 10 MCQs because of formula confusion and improper figure interpretation.
Some common mistakes include:
- Radius and diameter confusion
- CSA and TSA confusion
- Incorrect slant height usage
- Wrong formula selection
- Unit conversion mistakes
- Volume simplification errors
- Ignoring hidden surfaces in combined solids
Students should solve mensuration questions carefully instead of depending only on shortcuts.
Understanding Solid Shapes and Measurements in Simple Language
This chapter mainly focuses on measuring solid three-dimensional objects mathematically.
Unlike flat figures:
solid figures have height,
occupy space,
and contain volume.
For example:
a water bottle represents a cylinder,
an ice cream cone represents a cone,
a football represents a sphere,
and a bowl represents a hemisphere.
Students learn how to calculate:
outer surface covering,
storage capacity,
curved boundaries,
and total space occupied by these objects.
The chapter becomes easier when students connect formulas with real-life objects instead of memorizing calculations mechanically.
Important Formulas Used in Surface Areas and Volumes Class 10 MCQs
The following formulas are extremely important for solving Surface Areas and Volumes MCQs Class 10 and board exam questions.
| Shape | Formula |
|---|---|
| Volume of Cylinder | πr²h |
| Curved Surface Area of Cylinder | 2πrh |
| Total Surface Area of Cylinder | 2πr(r + h) |
| Volume of Cone | (1/3)πr²h |
| Curved Surface Area of Cone | πrl |
| Total Surface Area of Cone | πr(l + r) |
| Volume of Sphere | (4/3)πr³ |
| Surface Area of Sphere | 4πr² |
| Volume of Hemisphere | (2/3)πr³ |
| Total Surface Area of Hemisphere | 3πr² |
Students should revise these formulas regularly because many Surface Areas and Volumes Class 10 objective questions are directly calculation based.
Important Terms Students Must Understand
The following terms are very important for solving Surface Areas and Volumes Class 10 MCQs with Answers correctly.
| Term | Meaning |
|---|---|
| Radius | Distance from center to boundary |
| Diameter | Double of radius |
| Height | Vertical measurement of solid |
| Slant Height | Inclined height of cone |
| Curved Surface Area (CSA) | Outer curved covering only |
| Total Surface Area (TSA) | Complete outer surface |
| Volume | Total space occupied by solid |
Understanding these terms properly improves conceptual clarity and solving speed.
Understanding 3D Shapes Visually
One of the most important skills in this chapter is understanding how three-dimensional objects are formed and measured.
Students can improve shape understanding by:
- Observing real-life solid objects carefully
- Identifying curved and flat surfaces
- Comparing volume and surface area concepts
- Understanding height and radius relationships
- Practicing combined solid figure questions regularly
Once students become comfortable with shape visualization and formula selection, solving Surface Areas and Volumes Class 10 MCQs with Answers becomes much easier.
Revision Notes for Surface Areas and Volumes Class 10 MCQs
Students should revise these important points regularly before exams:
- Volume measures occupied space
- Surface area measures outer covering
- Radius is half of diameter
- CSA includes curved surfaces only
- TSA includes complete outer surface
- Slant height is important for cones
- Unit conversion requires attention
- Formula selection should be accurate
Short revision sessions help improve formula retention and board exam confidence significantly.
Final Summary
Practicing Surface Areas and Volumes Class 10 MCQs with Answers is one of the best ways to improve mensuration understanding, formula application, and three-dimensional geometry visualization for Class 10 Maths. This chapter is highly practical because students must understand solid figures, capacities, curved surfaces, and measurement relationships together instead of focusing only on direct calculations. Students preparing for CBSE board exams should focus on formula clarity, careful figure interpretation, and regular objective practice to improve confidence and solving speed naturally. Consistent practice of Surface Areas and Volumes Class 10 MCQs helps students strengthen practical geometry understanding, analytical reasoning, mathematical accuracy, and overall board exam performance effectively.