Mensuration Tricks: Area, Volume and Surface Area of 2D and 3D Shapes Questions for SSC CGL, CHSL
Rahul Kumar
SSC Exam Expert & Content Editor
In this note
PDF Notes: Mensuration Tricks: Area, Volume and Surface Area of 2D and 3D Shapes Questions for SSC CGL, CHSL
Premium PDF · one-time payment of ₹5 · instant access
Mensuration is the measurement of the length, area, surface area and volume of shapes. It is a regular 3 to 5 question topic in SSC CGL and CHSL maths, and every question is a direct use of a formula. These mensuration tricks for SSC give the formulas of 2D and 3D shapes in tables with a few shortcuts and solved questions.
2D Shapes
| Shape | Area | Perimeter |
|---|---|---|
| Square (a) | a² | 4a |
| Rectangle (l, b) | l × b | 2(l + b) |
| Triangle | ½ × base × height | Sum of the sides |
| Equilateral triangle (a) | (√3/4) a² | 3a |
| Circle (r) | πr² | 2πr |
| Parallelogram | base × height | 2(a + b) |
| Rhombus | ½ d₁ d₂ | 4a |
| Trapezium | ½(a + b) h | Sum of the sides |
3D Shapes
| Solid | Volume | Surface area |
|---|---|---|
| Cube (a) | a³ | 6a² |
| Cuboid (l, b, h) | lbh | 2(lb + bh + hl) |
| Cylinder | πr²h | Curved 2πrh, total 2πr(r + h) |
| Cone | ⅓πr²h | Curved πrl, total πr(r + l) |
| Sphere | (4/3)πr³ | 4πr² |
| Hemisphere | (2/3)πr³ | Curved 2πr², total 3πr² |
Shortcuts
- The diagonal of a square is a√2, and the diagonal of a cube is a√3.
- The slant height of a cone is l = √(r² + h²).
- If the radius of a circle is doubled, the area becomes 4 times.
- If the side of a cube is doubled, the volume becomes 8 times and the surface area 4 times.
- Use π = 22/7 when the radius is a multiple of 7.
Solved Examples
Example 1. Find the area of a circle of radius 7 cm (π = 22/7).
22/7 × 49 = 154 cm².
Example 2. Find the volume of a cylinder of radius 7 cm and height 10 cm.
22/7 × 49 × 10 = 1,540 cm³.
Example 3. Find the diagonal of a rectangle of 3 cm by 4 cm.
√(9 + 16) = 5 cm.
Example 4. Find the total surface area of a cube of side 2 cm.
6 × 4 = 24 cm².
Example 5. Find the area of an equilateral triangle of side 4 cm.
(√3/4) × 16 = 4√3 cm².
Example 6. Find the volume of a sphere of radius 3 cm.
(4/3) π × 27 = 36π cm³.
Example 7. By how much % does the area of a circle increase if its radius is increased by 10%?
The area becomes 1.1 × 1.1 = 1.21 times, so it increases by 21%.
Quick Tips
- Learn the formulas in two tables (2D and 3D).
- Use 22/7 when the radius is a multiple of 7.
- Check the units: square units for area and cubic units for volume.
- Use the percentage change in the area when a side or radius changes.
Quick Revision Points
- Area of a circle = πr².
- Volume of a cylinder = πr²h.
- Volume of a sphere = (4/3)πr³.
- Volume of a cone = ⅓πr²h.
- A cube with a doubled side has 8 times the volume.
Practice Questions With Answers
- Find the area of a circle of radius 7 cm (π = 22/7).
Answer: 154 cm² - Find the volume of a cube of side 3 cm.
Answer: 27 cm³ - Find the diagonal of a rectangle of 3 cm by 4 cm.
Answer: 5 cm - Find the total surface area of a cube of side 2 cm.
Answer: 24 cm² - Find the volume of a cylinder of radius 7 cm and height 10 cm.
Answer: 1,540 cm³ - Find the area of an equilateral triangle of side 4 cm.
Answer: 4√3 cm² - Find the volume of a sphere of radius 3 cm.
Answer: 36π cm³ - Find the circumference of a circle of radius 7 cm.
Answer: 44 cm - By how much does the area of a circle increase if its radius is increased by 10%?
Answer: 21% - If the side of a cube is doubled, how many times does its volume become?
Answer: 8 times
How to Practise This Chapter
Practise 10 questions every day and write the steps on paper. Then attempt timed sets from our practice papers and the previous year papers page. See all topics on the Mathematics notes page, read the previous topic Trigonometry Tricks. Formulas are in the Formula Guide and more practice is in the Quantitative Aptitude notes. Also read the Geometry and Mensuration Formula Guide.
Frequently Asked Questions
What is mensuration?
It is the measurement of the length, area, surface area and volume of shapes.
What is the area of a circle?
π times the radius squared.
What is the volume of a cylinder?
π r squared h.
What is the volume of a cone?
One-third of π r squared h.
What is the volume of a sphere?
Four-thirds of π r cubed.
What is the total surface area of a cube?
6 times the side squared.
What happens to the volume of a cube when the side is doubled?
The volume becomes 8 times.
Which value of π should I use?
Use 22/7 if the radius is a multiple of 7, otherwise 3.14.
Is mensuration asked in SSC exams?
Yes. It is asked in every SSC maths paper.
What are the common mistakes?
Mixing the curved and the total surface area, and using the diameter in place of the radius.
How much time should I take?
About 40 seconds.
How can I learn the formulas?
Write them on cards and solve one example for each.
Previous chapter
Trigonometry Tricks: Ratios, Identities, Height and Distance Questions for SSC CGL, CHSL
Next chapter
Triangles: Congruence, Similarity, Centres, Theorems and Formulas with Solved Examples for SSC CGL and CHSL Geometry
Rahul Kumar
SSC Exam Expert & Content Editor
Rahul is a senior SSC exam strategist with 8+ years of experience helping aspirants crack CGL, CHSL and MTS exams. He writes in-depth notification breakdowns, exam pattern guides and preparation strategies.