Topics Covered in Mensuration for CAT Exams

In CAT Geometry, mensuration is a topic that most students can understand. In addition to knowing fundamental formulas, one can ace Mensuration problems on the CAT exam by having a structural and spatial understanding of shapes. Mensuration includes a variety of 2D and 3D shapes, such as spheres, cubes, cuboids, cylinders, cones, and more. Mensuration will likely be the subject of at least one CAT exam question.

Mensuration’s importance in the CAT exam

• In the QA section of the CAT exam, there are 34 questions, and about 7 of them are about mensuration. In a competitive exam, five to seven questions are sufficient to determine one’s overall score

• Your ability to calculate and use numerology will be evaluated together with your accuracy when you answer questions about measurements in the QA section of the CAT exam.

• In the QA phase of the CAT exam, you get 40 minutes to answer 34 questions. Therefore, mensuration questions will also assess how quickly you can answer quantitative problems.

• In the CAT exam, each question has three marks. Mensuration questions are likewise worth three points apiece and have a significant impact on one’s final score and selection. Mensuration has numerous practical uses, such as figuring out how much it will cost to paint or renovate a structure or to install fencing.

Basic Mensuration Concepts

Area:

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.

• Area of Rectangle: Length X Breadth

• Area of Triangle: 0.5 X Base X Height

• Area of Square: Side X Side 

• Area of Circle: Pi X Radius X Radius

• Surface Area of a Cylinder = 2 X Pi X Radius X (Radius + Height)

• Surface Area of a Sphere = 4 X Pi X Radius X Radius

• Surface Area of a Cube = 6 X Side X Side

• Surface Area of a Cuboid = 2 X (Length X Breadth + Breadth X Height + Length X Height)

Volume:

The amount of space a shape or thing encloses, or the amount of three-dimensional space (length, breadth, and height) it takes up. This is expressed as a cubic unit, such as cm³, m³, etc.

• Volume of Cuboid: Length X Breadth X Height

• Volume of Cube: Side X Side X Side

• Volume of Sphere: 4/3 X Pi X Radius X Radius X Radius

• Volume of Prism: Area of Base X Height

• Volume of Cone: 1/3 X Pi X Radius X Radius X Height

Perimeter:

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)

Mensuration CAT Questions:

1. A plane cuts a sphere with radius r at a distance of h from its centre, splitting the sphere into two halves. These two parts together have a surface area that is 25% larger than the sphere’s. Find h.

• r/√2

• r/√3

• r/√5

• r/√6

2. At point P inside the circle, two chords AB and CD that are mutually perpendicular to one another meet. Here, AP = 6 cm, PB = 4 units, and DP = 3 units. What is the circle’s area?

• 125π/4 sq cms

• 100π/7 sq cms

• 125π/8 sq cms

• 52π/3 sq cms

3. The radius of an inverted right circular cone is 9 cm. Oil is dripping from a hole in the tip of this cone at a rate of 1 cm per hour, partially filling the cone. Currently, there is 3 cm of oil above the surface, covering 36 cm2. How much time will it take the cone to empty completely?

• 72π hours

• 1 hour

• 3 hours

• 36π hours

4. A sphere-shaped sweet is inserted into a 5-cm-square cube so that it barely fits. On one of the cube’s vertices, a fly is perched. How far can the fly fly to get to the sweet in the shortest amount of time?

• 2.5 cm

• 5(√3 – 1) cm

• 5(√2 – 1) cm

• 2.5(√3 – 1) cm

Conclusion

For the purpose of comprehending the idea of Area and Perimeter of Plane Figures (triangle, rectangle and square). Rectangle area and perimeter calculations using the reacting angel and square are covered. We must learn mensuration in order to calculate the area and circumference of a circle.

It assists us in determining the volume of a three-dimensional object, such as when determining the water tank’s capacity. It also aids in measuring the surface areas of 3D objects, such as when painting a building’s interior or exterior walls. Additionally, it aids in building.