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CAT Mensuration is one of the geometry topics. Aspirants should excepts at least 5-6 questions for mensuration. As quantitative section contain total 34 question and out of that 5-6 are mensuration problems. Mensuration is all most formula based topic. Clearing your mensuration concepts will enhance your accuracy level in exam. Hence, Pay attention to concepts and formula’s. As you all know geometry topic contain 10% of weightage in CAT exam.
In this article, we learn about some the important dimensions of CAT mensuration. All important aspects related to the topic will be covered. Aspirant would understand how to approach question when his concepts become clear. In addition one could easily ace mensuration just by formula’s and basic concepts clarity.
Mensuration questions per exam based on past trends 2020-2025
| Year | CAT | XAT | NMAT | SNAP | CET | Total per Year |
|---|---|---|---|---|---|---|
| 2020 | 3 | 2 | 2 | 1 | 3 | 11 |
| 2021 | 3 | 2 | 1 | 2 | 2 | 10 |
| 2022 | 2 | 1 | 2 | 1 | 4 | 10 |
| 2023 | 3 | 2 | 2 | 2 | 3 | 12 |
| 2024 | 3 | 3 | 1 | 1 | 2 | 10 |
| 2025 | 2 | 2 | 2 | 1 | 3 | 10 |
| Total | 16 | 12 | 10 | 8 | 17 | 63 |
Mensuration basic concepts for CAT exam
Mensuration is a branch of mathematics. That teaches us about the length, volume, or area. And tell us about different geometric shapes. These shapes exist 2 forms. Namely 2 dimensions or 3 dimensions. Let us known about it further. First aspirant should known the difference between these two dimensions.
Differences Between 2D and 3D dimensions.
| 2D dimension | 3D dimension |
|---|---|
| If a shape is surrounded by three or more straight lines in a plane, then it is a 2D dimension | If a shape is surrounded by a no. of surfaces or planes then it is a 3D dimension |
| These shapes have no depth or height. | These are also called solid shapes and unlike 2D they have height or depth. |
| These shapes have only two dimensions say length and breadth. | These are called Three dimensional as they have depth (or height), breadth and length. |
| We can measure their area and Perimeter. | We can measure their volume, CSA, LSA or TSA. |
Important Terminologies of Mensuration for CAT exam.
| Terminologies | Abbreviation examiner could use. | Unit in which answer should denoted. | Explanation |
| Area | A | m2 or cm2 | The area is the surface which is covered through the closed shape. |
| Perimeter | P | cm or m | The measure of the continuous line along the boundary of the given figure. |
| Volume | V | cm3 or m3 | The space occupied by a 3D shape is called a Volume. |
| Curved Surface Area | CSA | m2 or cm2 | If there’s a curved surface, then Curved Surface Area is the total area. For Example: Sphere |
| Lateral Surface area | LSA | m2 or cm2 | Lateral Surface area is the total area of all the lateral surfaces that surrounds the given figure. |
| Total Surface Area | TSA | m2 or cm2 | Total Surface area is the sum of all the curved and lateral surface areas. |
| Square Unit | – | m2 or cm2 | A Square unit is the area covered by a square of side one unit. |
| Cube Unit | – | m3 or cm3 | The volume occupied by a cube of one side one unit |
2D Shape Important Formula’s of mensuration for CAT exam.
Learn these formula’s. These formula’s would help you in solving formula based questions. Paste this table on your study table so you could revise them on regular basics. Lets have a look on below mention table:
Area of shapes
An expression of the size of a two-dimensional surface or shape in a plane is the term “area.” This is measured in square unit like cm2, m2, etc.
- To calculate Area of Rectangle. Use this formula = Length X Breadth
- To calculate Area of Triangle. Use this formula = 0.5 X Base X Height
- To calculate Area of Square. Use this formula =Side X Side
- To calculate Area of Circle. Use this formula =Pi X Radius X Radius
- To calculate Surface Area of a Cylinder. Use this formula = 2 X Pi X Radius X (Radius + Height)
- To calculate Surface Area of a Sphere. Use this formula = 4 X Pi X Radius X Radius
- To calculate Surface Area of a Cube. Use this formula = 6 X Side X Side
- To calculate Surface Area of a Cuboid. Use this formula = 2 X (Length X Breadth + Breadth X Height + Length X Height)
Perimeter of shapes:
A perimeter is a path that surrounds a two-dimensional shape, it’s SI unit will be the meter itself.
- Perimeter of Circle: 2 X Pi X Radius
- Perimeter of Triangle: Side A + Side B + Side C
- Perimeter of Square: 4 X Side
- Perimeter of Rectangle: 2 X (Length + Breadth)
3D Shape Important Formula’s of mensuration for CAT exam.
These formula’s would help you in solving formula based questions. Paste this table on your study table so you could revise them on regular basics.
| Shapes | Total Surface Area | Lateral/ Curved Surface area | Volume | Length of Leading Diagonal/ Slant Height |
| Cube | 2(LB+ BH+ HL) | 2H (L + B) | LBH | √ (L2 + H2 + B2) |
| Cuboid | 6a2 | 4a2 | a3 | √3a |
| Cylinder | 2Πr (r + h) | 2Πrh | Πr2h | No Slant height or diagonal |
| Cone | Πr (r + l) | Πrl | ⅓Πr2h | √(h2 + r2) |
| Sphere | 4Πr2 | 4Πr2 | 4/3Πr3 | No Slant height or diagonal |
| Hollow Cylinder | 2Π(r₁+r₂) (r₂-r₁+h) | 2Πh(r₁+r₂) | Πh(r₂²-r₁²) | No Slant height or diagonal |
| Frustum | Π(R1 + R2)s + (R12 + R22) | Π(R1 + R2)s | ⅓Πh(R12 + R22 + R1R2) | √(h2 + (R1 – R2)2) |
| Hemisphere | 3Πr2 | 2Πr2 | 2/3Πr3 | No Slant height or diagonal |
Important past year question from CAT exam.
1. A solid right circular cone of height 27 cm is cut into pieces along a plane parallel to its base at a height of 18 cm from the base. If the difference in volume of the two pieces is 225 cc, the volume, in cc, of the original cone is
A) 243 B) 232 C) 256 D) 264 [CAT 2020]
Solution: If height becomes 1/3rd then radius also becomes 1/3rd
If both height and radius become 1313rd, Volume will be 1/27th
So, Top part’s volume = V
Remaining part = 26V
Totally = 27V
Given 26 V – V = 225
Hence, V = 9
2. The length, breadth, and height of a room are in the ratio 3:2:1. If the breadth and height are halved while the length is doubled, then the total area of the four walls of the room will (CAT 19 – Slot 1)
1. Remain the same
2. Dec. by 13.64%
3. Dec. by 15%
4. Dec. by 18.75%
5. Dec. by 30%
Solution: in the present case, let length = l = 3x, breadth = b = 2x, height = h = x
then, area of four walls = 2 (l + b) h = 2(3x + 2x) x = 10×2.
now as length gets doubled = 6x, breadth halved = x, height halved = x/2.
new area of four walls = 2 (6x + x) x/2 = 7×2.
thus there is a decrease of 30%. hence, the fifth option is the answer.
3. Corners are cut off from an equilateral triangle T to produce a regular hexagon H. Then, the ratio of the area of H to the area of T is
A) 3:4 B) 2:3 C) 5:6 D) 4:5 [CAT 2019]
Solution: In given case , figure can be drawn as below
Let side of equilateral triangle ABC = 3a
So side of hexagon = a
Area of triangle = (root3 /4 )*(3a)^2 = 9a^2 *(root3/4)
Area of hexagon with side a = 6*(root3 /4 )*(a)^2
Ratio of areas of hexagon to that of triangle = { 6*(root3 /4 )*(a)^2 } / { 9a^2 *(root3/4)} = 6/9 = 2/3
Thus required ratio = 2 : 3
4. A man makes complete use of 405 cc of iron, 783 cc of aluminium, and 351 cc of copper to make a number of solid right circular cylinders of each type of metal. These cylinders have the same volume and each of these has radius 3 cm. If the total number of cylinders is to be kept at a minimum, then the total surface area of all these cylinders, in sq cm, is [CAT 2019]
A) 8464π B) 928π C) 1026(1 + π) D) 1044(4 + π)
Solution: As cylinders have the same volume and each of these has radius 3 cm. So volume of each cylinder will be equal to HCF of (405, 783 and 351) which is 27.
So volume of each cylinder = 27
No of cylinders = [ 405/27 ] + [783/27] + [351/27] = 15 + 29 + 13 =57
Using V = πr^2 h
27 = 22/7 *9 *h
So h = 3/ π cm.
CAT Mensuration PYQs (2020–2025)
1 ) A solid right circular cone of height 27 cm is cut into two parts by a plane parallel to its base at a height of 18 cm from the base. If the difference in volume of the two parts is 225 cc, then the volume (in cc) of the original cone is
A) 243
B) 232
C) 256
D) 264
[CAT 2020]
2) The length, breadth, and height of a room are in the ratio 3:2:1. If the breadth and height are halved while the length is doubled, then the total area of the four walls of the room will
A) Remain the same
B) Decrease by 13.64%
C) Decrease by 15%
D) Decrease by 18.75%
E) Decrease by 30%
[CAT 2020]
3) A cube is painted on all its faces and then cut into 64 smaller cubes of equal size. How many of these smaller cubes have exactly two faces painted?
A) 12
B) 24
C) 36
D) 48
[CAT 2021]
4) A cylindrical tank of radius 7 cm is completely filled with water. A solid sphere of radius 7 cm is immersed in the tank. The increase in the water level (in cm) is
A) 2
B) 4/3
C) 8/3
D) 3
[CAT 2021]
5) A solid cube is melted and recast into smaller cubes each having half the side length of the original cube. The number of smaller cubes formed is
A) 4
B) 6
C) 8
D) 12
[CAT 2022]
6) A cone and a cylinder have the same base radius and height. The ratio of the volume of the cone to that of the cylinder is
A) 1 : 2
B) 1 : 3
C) 2 : 3
D) 3 : 1
[CAT 2022]
7) A frustum of a cone is formed by cutting a cone with a plane parallel to its base. If the radii of the two circular ends are 3 cm and 6 cm and the height is 9 cm, then the volume (in cm³) is
A) 189π
B) 243π
C) 297π
D) 324π
[CAT 2023]
8) A wire of length 44 cm is first bent into a square and then reshaped into a circle. The ratio of the areas of the circle to that of the square is
A) 11 : 14
B) 14 : 11
C) 22 : 7
D) 7 : 22
[CAT 2023]
9) A hollow cylinder has an external radius of 10 cm and internal radius of 7 cm. If its height is 14 cm, then the volume (in cm³) of the material used is
A) 924π
B) 1323π
C) 1848π
D) 2310π
[CAT 2024]
10) A sphere of radius 6 cm is melted and recast into smaller spheres of radius 3 cm each. The number of smaller spheres formed is
A) 4
B) 6
C) 8
D) 12
[CAT 2024]
11) A rectangular park of length 50 m and breadth 30 m is surrounded by a uniform path of width 5 m. The area (in m²) of the path is
A) 800
B) 900
C) 1000
D) 1100
[CAT 2025]
12) The radius of a circle is increased by 20%. The percentage increase in its area is
A) 36%
B) 40%
C) 44%
D) 48%
[CAT 2025]
13) A cube of side 12 cm is cut into smaller cubes each of side 3 cm. How many cubes are formed?
A) 16
B) 32
C) 64
D) 128
[CAT 2025]
14) A right circular cylinder and a sphere have the same radius and volume. The ratio of the height of the cylinder to the radius is
A) 2 : 3
B) 3 : 2
C) 4 : 3
D) 3 : 4
[CAT 2025]
15) A triangle has base and height increased by 20% each. The percentage increase in its area is
A) 20%
B) 36%
C) 40%
D) 44%
[CAT 2025]
Mensuration is not just about formulas it’s about smart application and pattern recognition. With consistent practice and the right strategy, you can easily convert this topic into a high-scoring advantage in CAT.
If you’d like to explore structured preparation, you can visit the CAT courses page where both the Quant Sectional Course for 2026 and full program details are available to review at your own pace
Frequently Asked Questions
1. How many questions from Mensuration are asked in CAT?
Mensuration contributes around 5–6 questions in the CAT exam under the Quantitative Aptitude section. It forms a part of Geometry, which has approximately 10% overall weightage.
2. Is Mensuration an easy topic for CAT preparation?
Yes, Mensuration is considered relatively easy because it is mostly formula-based. With proper understanding and practice, it can become a high-scoring area.
3. What are the most important Mensuration topics for CAT?
Key topics include:
- Area and perimeter of 2D shapes
- Volume and surface area of 3D shapes
- Cylinders, cones, spheres
- Frustum and hollow solids
- Mensuration-based word problems
4. How should I prepare Mensuration for CAT effectively?
To prepare effectively:
- Learn all basic formulas thoroughly
- Practice previous year questions (PYQs)
- Focus on shortcut techniques and ratios
- Revise regularly
5. Are formulas enough to solve CAT Mensuration questions?
Formulas are important, but not sufficient alone. You also need:
- Concept clarity
- Ability to identify patterns and shortcuts
- Practice with application-based questions
6. Do CAT Mensuration questions involve lengthy calculations?
Generally, CAT focuses on logic and concept application, not heavy calculations. Many questions can be solved using ratios, approximations, and shortcuts.
7. What is the difference between 2D and 3D Mensuration?
- 2D Mensuration: Deals with area and perimeter (e.g., square, triangle)
- 3D Mensuration: Deals with volume and surface area (e.g., cube, cylinder, sphere)
8. Which formulas are most important to remember for CAT Mensuration?
Important formulas include:
- Area of circle, triangle, rectangle
- Volume of cube, cylinder, cone, sphere
- Surface areas (CSA, TSA, LSA)
- Ratio relationships in similar figures
9. How much time should I dedicate to Mensuration?
You should spend around 1–2 weeks to build strong concepts and then continue practicing regularly through mocks and sectional tests.
10. Can Mensuration help improve overall CAT percentile?
Yes, absolutely. Since it is a predictable and scoring topic, strong preparation in Mensuration can significantly boost your accuracy and overall percentile.
Also read:
Crack CAT Quants with a 99 Percentile Strategy: Insights from an IIM Ahmedabad Alumni
Important Quant topics for CAT
CAT 2026 Preparation Strategy: 8-Month Study Plan for Engineers & Non-Engineers
Most difficult topics in Quants
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