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Important Geometry Formulas for CAT Exam
Geometry is one of the most important and recurring topics in the CAT Quantitative Aptitude section. Questions are generally based on properties, visualization, and application of formulas rather than direct substitution. Hence, knowing the core formulas is essential.
2D Geometry Formulas for CAT
Shape | Formula Type | Formula |
Square | Area | a² |
Perimeter | 4a | |
Diagonal | √2 a | |
Rectangle | Area | l × b |
Perimeter | 2(l + b) | |
Diagonal | √(l² + b²) | |
Parallelogram | Area | base × height |
Perimeter | 2(a + b) | |
Triangle | Area | ½ × base × height |
Heron’s Formula | √[s(s-a)(s-b)(s-c)] | |
Equilateral Area | √3/4 a² | |
Perimeter | a + b + c | |
Right Triangle | Pythagoras Theorem | a² + b² = c² |
Circle | Area | πr² |
Circumference | 2πr | |
Arc Length | (θ/360) × 2πr | |
Sector Area | (θ/360) × πr² | |
Trapezium | Area | ½ × (sum of parallel sides) × height |
Rhombus | Area | ½ × d₁ × d₂ |
Polygon (n sides) | Sum of Interior Angles | (n − 2) × 180° |
3D Mensuration Formulas for CAT
Solid | Formula Type | Formula |
Cube | Volume | a³ |
Total Surface Area | 6a² | |
Diagonal | √3 a | |
Cuboid | Volume | l × b × h |
Total Surface Area | 2(lb + bh + hl) | |
Diagonal | √(l² + b² + h²) | |
Cylinder | Volume | πr²h |
Curved Surface Area | 2πrh | |
Total Surface Area | 2πr(r + h) | |
Cone | Volume | 1/3 πr²h |
Curved Surface Area | πrl | |
Total Surface Area | πr(l + r) | |
Sphere | Volume | 4/3 πr³ |
Surface Area | 4πr² | |
Hemisphere | Volume | 2/3 πr³ |
Total Surface Area | 3πr² |
Download Free CAT Geometry Formulas PDF
To help you revise quickly before mocks and the CAT exam, we have compiled all important CAT Geometry formulas, key theorems, and shortcut concepts into one easy-to-use PDF. It covers 2D and 3D mensuration formulas along with quick revision notes. Download the free CAT Geometry Formulas PDF and use it for regular practice and last-minute revision.
CAT Geometry Questions with Solutions
Question 1
Let ABC be an isosceles triangle. Suppose that the sides AB and AC are equal and let the length of AB be x cm. Let b denote the angle ∠ABC and sin b = 3/5. If the area of the triangle ABC is M square cm, then which of the following is true about M?
correct answer:- 5
Question 2
In a building there are 30 cylindrical pillars. The radius of each pillar is 35 cm and height is 5 m. Find out the cost of painting the curved surface of half the number of pillars. The rate of painting is Rs. 10 per $$m^2$$.
correct answer:- 3
Question 3
In a triangle ABC, AD is the bisector of angle A. If AC =4.2 cm, DC = 6 cm, BC =10 cm, find AB.
correct answer:- 3
Question 4
The maximum value of 3 $$cosx+4 sinx+8$$ is
correct answer:- 3
Question 5
The length, breadth and height of a rectangular cuboid are in the ratio 1: 2 : 3. If the length, breadth and height are increased by 100% each then what would be the increase in the volume of the cuboid ?
correct answer:- 2
Question 6
It costs Rs. 6000/- and Rs. 6,100- respectively to paint the 4 walls of 2 square halls, of the same height. If the length of one hall exceeds the length of the other by 1 m and the cost of painting is Rs. 5 per sq.m., what is the height of the two walls ?
correct answer:- 4
Question 7
A rectangular box of width(a), length(b), and height(c) has a solid cylinder of height 'c' and of diameter 'a' placed within it. If a= 6, b =8 and c =10, how much volume is left in the rectangular box ?
correct answer:- 4
Question 8
Three solid cubes of sides 1 cm, 6 cm and 8 cm are melted to form a new cube. Find the surface area of the cube so formed.
correct answer:- 2
Question 9
How many iron balls, each of radius 1 cm, can be made from a sphere whose radius is 8 cm?
correct answer:- 3
Question 10
In a circle of radius 6 cm, arc AB makes an angle of 114° with centre of the circle O.
What is angle ABO?
correct answer:- 4
Question 11
The length of the minute of a watch is 42 mm. The area swept by it in 30 minutes (in $$mm^2$$) by taking π as 3.14 is:-
correct answer:- 1
Question 12
The length of a room exceeds its breadth by 2 meters. If the length be increased by 4 meters and the breadth decreased by 2 meters, the area remains the same. Find the surface area of its walls if the height is 3 meters.
correct answer:- 4
Question 13
If the height of a right circular cone is increased by 200% and the radius of the base is reduced by 50%, then the volume of the cone.
correct answer:- 2
Question 14
In the figure, PQ is a diameter of the circle. Angle PQS = $$35^\circ$$. Find angle QRS.
correct answer:- 1
Question 15
The area of a triangle metal plate with base 88 cm and altitude 64 cm is to be reduced to one-fourth of its original area by making a hole of circular shape at the center. The radius of this hole will be:-
correct answer:- 4
Question 16
The sides of triangle are 3 consecutive even integers with the largest side being less than 13. What is the total number of such triangles?
correct answer:- 3
Question 17
The interior angles of a convex polygon are in arithmetic progression. The smallest angle is 120° and the common difference is 5°. Then the number of its sides is
correct answer:- 2
Question 18
The diameter of the circumcircle of the triangle formed by the line $$24x + 7y =168$$ and the coordinate axes is
correct answer:- 3
Question 19
The area enclosed between the parabolas $$y^2 = 16(1 + x )$$ and $$y^2 = 16(1 - x)$$ is
correct answer:- 3
Question 20
The foot of the ladder RS in the following figure is slipping away from the wall RO.
Then the point P(a fixed point on the ladder) lies on
correct answer:- 4
CAT Geometry Questions Preparation Strategy
Geometry in CAT is concept-driven and requires clarity, visualization, and regular practice. Follow this structured strategy to improve accuracy and speed:
- Strengthen Your Basics: Revise all important 2D and 3D mensuration formulas thoroughly. Make sure you are comfortable with areas, volumes, diagonals, triangle properties, and circle formulas.
- Build Strong Conceptual Clarity: Focus on understanding triangle similarity, properties of quadrilaterals, circles, coordinate geometry basics, and key theorems. CAT questions test application, not just formulas.
- Practice CAT-Level Questions Regularly: Solve previous year CAT questions and sectional tests. This helps you understand question patterns and difficulty levels.
- Improve Visualization Skills: Always draw neat and accurate diagrams. Many mistakes happen because of incorrect assumptions or poor figures.
- Analyze Mistakes Deeply: After every mock or practice set, review wrong answers carefully. Identify whether the mistake was conceptual, calculation-based, or due to misinterpretation.
- Revise Consistently: Use a CAT Geometry Formulas PDF for quick revision before mocks and during the final preparation phase.
CAT Geometry Formulas with Practice Questions: Conclusion
Geometry is a scoring but concept-based topic in CAT Quant. Just memorizing formulas is not enough. You need clear concepts, good visualization, and regular practice with CAT-level questions. Revising 2D and 3D mensuration formulas frequently will help improve your speed and accuracy in mocks and the final exam.
To score well in CAT Geometry, understand the properties of triangles, quadrilaterals, circles, polygons, and 3D shapes. Follow a proper study plan, analyze your mistakes after every mock, and revise from a reliable CAT Geometry formulas PDF. With consistent practice, Geometry can become one of your strongest sections in CAT Quant.
