Important AREA & VOLUME Formulas for Quant

In this post, we are going to have a look at all the Important Area & Volume Formulas for Quant section asked in various competitive exams. We also try and and understand what is a Quantitative Aptitude test,

Quantitative Aptitude Test

This test is performed to assess how mentally capable a candidate is by monitoring how they perform a particular gives task and reacts to certain situations. A standard method is applied for both administration and marking in order to calculate the results and compare them with the results of other candidates. The aim is to assess how well the candidate will be able to perform their duties and face the challenges of the career. 

Process of an Aptitude Test

These tests are conducted online as the process of a job interview or a competitive examination. The aim of an aptitude test before an interview is to separate the suitable candidates from others and make it easier to finalize the most suitable candidate for the job. The primary intention is to find out if the candidate is capable of facing the job challenges and shoulder the responsibilities of the post. Sometimes aptitude tests are also taken as an offline written examination.

Structure of the Test

These tests are time-bound and contain multiple-choice questions. The provided options are often misleading, so the candidate should be very alert and attentive while going through an aptitude test. In certain cases, as the test progresses, the questions become increasingly difficult. Such tests are not expected to be completed, and the marking increases with the rise in the level of difficulty.

Marking and scores of the test

The qualifying marks are set considering that every individual is not an expert in all the fields/ areas of an aptitude test. The qualifying score is calculated considering an average score of all the sections of an aptitude test. 

Also Read:  Quicker Maths Tricks PDF [Topic-Wise] – Learn Fast Calculation Tricks

Negative marking

In some aptitude tests, negative marking is considered by deducting some marks from the total score for wrong answers. In such a case, answer only if you are certain that it is correct. Please do not rely on guesswork, as it can bring down your score. 

Step to solve an Aptitude Test

• You must go through the information thoroughly.
• Think and analyze the given information.
• Apply the formula or concept for the given situation.
• Evaluate and verify your calculation.
• Select the correct answer 

Important AREA & VOLUME Formulas 

Surface Area and Volume

Surface area and volume are calculated for 3D geometric shapes. The area covered by any given object is its surface area, and the space available in that object it’s its volume.

There are different shapes and sizes in geometry (like cuboid, cube, cylinder, sphere, cone, etc.), and each has its own surface area and volume. Only the surface area can be calculated in the case of 2D figures (like Rectangle, square, triangle, circle, etc.).

The area occupied by a 3D object is called it’s surface area whereas, the space occupied by a 2D figure is called its area. Both are measured in square units.

Area is of two types

(i) Total Surface Area

(ii) Curved Surface Area/Lateral Surface Area

AREA & VOLUME Formulas

Area of a Triangle

Area= ½ x b x h

Where, 

b = base

h = height 

Area of a Rectangle

Area= l x b

Where, l = length, and b= breadth.

Area of a Trapezium

Area= ½  x (sum of the length of  parallel sides) x perpendicular distance between the parallel sides

Area of a Circle

Area= πr²

Where, 

π = 22/7 or 3.14

r = radius 

Area of Equilateral Triangle

Area= (√3/4)a²

Area of square 

Area= Side²  square units

Area of parallelogram

Area = b × h Square units

Where, b=  base of the parallelogram

             h = height of the parallelogram.

Area of Rhombus

The different formulas to calculate the area of a rhombus are:

1. Using Diagonals
   Area= ½ × d₁ × d₂
2. Using the base and Height
   Area= b x h
3. Using Trigonometry
   Area= b² × Sin(a)

Where,

1. d₁ = length of diagonal 1
2. d₂ = length of diagonal 2
3. b = length of any side
4. h = height of rhombus
5. a = measure of any interior angle

Area of Sphere:

Let r be the radius of the sphere. Then:

1. The volume of the sphere = 4/3 πr³cubic units.
2. The surface area of the sphere is 4 π r²sq. units.
3. Curved surface area of the hemisphere = (2 πr²) sq. units.
4. Whole surface area of the hemisphere = (3 πr²) sq. units.

Area of Cube

Let each edge of a cube = “a” units. Then:

1. The whole surface area of cube = (6a²) sq. units.
2. Diagonal of the cube (√3a)

Area of Cylinder

Let the radius of the base of a cylinder be r units, and the height of the cylinder be h units. Then:

1. Curved surface area of cylinder = (2πrh) sq. units.
2. Total surface area of cylinder =(2πrh 2πr²) sq. units.

Area of Isosceles Triangle

The different formulas to calculate the area of an isosceles triangle are:

• Using the base and height
  Area= ½ × b × h
• Using all three sides
  Area= ½[√(a² − b² ⁄4) × b]
• Using the length of 2sides and the angles b/w them
  Area= ½ × b × c × sin(α)
• Using 2 angles and the length b/w them
  Area=  [c²×sin(β)×sin(α)/ 2×sin(2π−α−β)]
• Area of an isosceles right triangle 
  Area= ½ x a²
• Area of Isosceles Triangle Using Only Sides
  Area=  ½[√(a² − b² /4) × b]

Here,

• b = base of the isosceles triangle
• h = height of the isosceles triangle
• a = length of the two equal sides

Volume of Cylinder

The volume of the cylinder = (πr² h) cubic units.

Volume of Sphere

The volume of a sphere = 4/3 πr³

Volume of Cone

The volume of the cone (1/3) πr²h cubic units.

Volume of cube

The volume of the cube = a³ cubic units.

Volume of cuboid

Volume of cuboid = (l x b x h) cubic units

Volume of Hemisphere

The volume of a hemisphere is 2πr³/3 cubic units.

Area of Cuboid

Let length = l, breadth = b, and height = h units

1. Whole surface area of cuboid = 2 (lb bh hl) sq. units.
2. Diagonal of cuboid =  =√( l2 b2 h2)units.

Surface Area of Right circular cone

Let r be the radius of the base, h is the height, and l is the slant height of the cone.

 Then:

1. The curved surface area of right circular cone = π r l
2. The total surface area of a right circular cone = π(r  l) r
3. The volume of a right circular cone = 1/3π r² h

That is all from us in this post on Important Area and Volume Formulas for Bank, SSC, Railway Exams like SBI PO, IBPS PO, SSC CGL, IBPS Clerk, SBI Clerk, Railway Group D, SSC CHSL, etc.