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
- Important AREA & VOLUME Formulas
- Surface Area and Volume
- AREA & VOLUME Formulas
- Area of a Triangle
- Area of a Rectangle
- Area of a Trapezium
- Area of a Circle
- Area of Equilateral Triangle
- Area of square
- Area of parallelogram
- Area of Rhombus
- Area of Sphere:
- Area of Cube
- Area of Cylinder
- Area of Isosceles Triangle
- Volume of Cylinder
- Volume of Sphere
- Volume of Cone
- Volume of cube
- Volume of cuboid
- Volume of Hemisphere
- Area of Cuboid
- Surface Area of Right circular cone
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.
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
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
π = 22/7 or 3.14
r = radius
Area of Equilateral Triangle
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:
- Using Diagonals
Area= ½ × d1 × d2
- Using the base and Height
Area= b x h
- Using Trigonometry
Area= b2 × Sin(a)
- d1 = length of diagonal 1
- d2 = length of diagonal 2
- b = length of any side
- h = height of rhombus
- a = measure of any interior angle
Area of Sphere:
Let r be the radius of the sphere. Then:
- The volume of the sphere = 4/3 πr³cubic units.
- The surface area of the sphere is 4 π r2sq. units.
- Curved surface area of the hemisphere = (2 πr2) sq. units.
- Whole surface area of the hemisphere = (3 πr2) sq. units.
Area of Cube
Let each edge of a cube = “a” units. Then:
- The whole surface area of cube = (6a2) sq. units.
- 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:
- Curved surface area of cylinder = (2πrh) sq. units.
- 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]
- b = base of the isosceles triangle
- h = height of the isosceles triangle
- a = length of the two equal sides
DOWNLOAD THE OLIVEBOARD APP FOR ON-THE-GO EXAM PREPARATION
- Video Lessons, Textual Lessons & Notes
- Topic Tests covering all topics with detailed solutions
- Sectional Tests for QA, DI, EL, LR
- All India Mock Tests for performance analysis and all India percentile
- General Knowledge (GK) Tests
Free videos, free mock tests and free GK tests to evaluate course content before signing up!
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
- Whole surface area of cuboid = 2 (lb bh hl) sq. units.
- 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.
- The curved surface area of right circular cone = π r l
- The total surface area of a right circular cone = π(r l) r
- 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.