Important Formula: Volume, Surface Area & Solid Figures

# Important Formula: Volume, Surface Area & Solid Figures | Quantitative Aptitude for SSC CGL PDF Download

## Perimeter, Area and Volume formulas for various shapes

• Geometry, a branch of mathematics, focuses on diverse shapes and sizes. It can be categorized into two types: Plane Geometry and Solid Geometry.
• Plane Geometry involves shapes like circles, triangles, rectangles, and squares.
• Solid Geometry is dedicated to calculating the length, perimeter, area, and volume of various geometric figures and shapes. Presented below are some fundamental formulas used to compute the length, area, volume, and perimeter of diverse shapes and figures.

## Formulas For Perimeter Area Volume

### Formulas for Square

• Here, s = side
• Perimeter: 4 * s
• Area: S2
• Diagonal: s√2
• Area of square when diagonal is given

### Formulas for Rectangle

• Here , l = length, b = breadth.
• Perimeter: 2 (l + b) (l = length, b = breadth)
• Area: l × b
• Diameter:
• Area of 4 walls of a room = 2 (Length + Breadth) × Height

### Formulas of Circle

• Area of circle = πr²
• Area of semi-circle= πr2/2
• Circumference of a circle = 2πr
• Circumference of a semi-circle = πr
• Length of arc
• Area of sector = 1/2 (arc*R) = πr²ɵ/360

### Parallelogram formulas

• Perimeter: 2(a + b)
• Area: b × h
• Height of parallelogram = A/b

### Rhombus formulas

• Perimeter: 4 × a
• Area:
• Diagonals

### Trapezium formulas

• Perimeter: a + b + c + d
• Area: 1/2  × (sum of parallel sides) × distance between them
• To find thee distance between parallel sides you will have to convert trapezium to rectangle and then use Pythagoras Theorem.

### Cube formulas

• Volume: (side)3
• Surface area = 6s2
• Partial Surface area = 4s2
• Diagonal = √3s

### Cuboid formulas

• Volume: l * b * h
• Surface area = 2 (lb + bh + hl)
• Curved Surface area = 2h(l+b)
• Diagonal =

### Sphere formulas

Formulas for Sphere

• Volume:
• Surface area = 4πr2

### Hemisphere formulas

• Volume:
• Curved Surface area = 2πr²
• Total Surface area = 3πr²

### Cylinder formulas

• Volume: πr²h
• Curved Surface area = 2πrh
• Total Surface area = 2πr (h + r)

### Cone formulas

• Volume:
• Slant height
• Curved Surface area = πrl
• Total Surface area = πrl +πr

## Some Examples Based On Above Formulas

Q1: Rohan Bought a House, which had a garden outside it, with sides measuring 12 meters and 8 meters, Find the perimeter of the  garden ?
Ans: The formula to find Perimeter is , P= 2(L+W)
= 2(12+8)
=2(20)
=40m Ans.

Q2: Two kids planned to make an equilateral traingle  of a cardboard , The length of one side of  the traingle being  8 centimeters. Calculate the perimeter of the triangle.
Ans:
Perimeter  of Equilateral Traingle = 3 x Side length
= 3 x 8
= 24m Ans

Q3: The base of a triangle measures 12 centimeters, and its height is 8 centimeters. Find the area of the triangle.
Ans:
Area of the triangle = (Base × Height) / 2
= (12 centimeters × 8 centimeters) / 2
= 48 square centimeters.

Q4: To protect his house from Robbers, Mohan wrapped a wire around his square plot. If the wire’s length is 80 meters, what is the perimeter of the square?
Ans:
Perimeter of Square Plot = 4a(Where a = length of side)
= 4 x 80
= 320m Ans.

Q5: Rahul Came up with an idea to make figure made up of two adjacent rectangles, one measuring 8 meters by 5 meters and the other 6 meters by 4 meters. Find the total area of the figure.
Ans:
Total area of the figure = Area of the first rectangle + Area of the second rectangle
= (8 meters × 5 meters) + (6 meters × 4 meters)
= 40 square meters + 24 square meters
= 64 square meters.

The document Important Formula: Volume, Surface Area & Solid Figures | Quantitative Aptitude for SSC CGL is a part of the SSC CGL Course Quantitative Aptitude for SSC CGL.
All you need of SSC CGL at this link: SSC CGL

## Quantitative Aptitude for SSC CGL

314 videos|170 docs|185 tests

## FAQs on Important Formula: Volume, Surface Area & Solid Figures - Quantitative Aptitude for SSC CGL

 1. What is the formula for finding the volume of a rectangular prism?
Ans. The formula for finding the volume of a rectangular prism is length x width x height.
 2. How do you calculate the surface area of a cylinder?
Ans. The formula for calculating the surface area of a cylinder is 2πr² + 2πrh, where r is the radius of the base and h is the height of the cylinder.
 3. What is the formula for finding the volume of a cone?
Ans. The formula for finding the volume of a cone is 1/3πr²h, where r is the radius of the base and h is the height of the cone.
 4. How do you find the surface area of a sphere?
Ans. The formula for finding the surface area of a sphere is 4πr², where r is the radius of the sphere.
 5. What is the formula for finding the volume of a pyramid?
Ans. The formula for finding the volume of a pyramid is 1/3Bh, where B is the base area and h is the height of the pyramid.

## Quantitative Aptitude for SSC CGL

314 videos|170 docs|185 tests

### Up next

 Explore Courses for SSC CGL exam

### Top Courses for SSC CGL

Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
10M+ students study on EduRev
Related Searches

,

,

,

,

,

,

,

,

,

,

,

,

,

,

,

,

,

,

,

,

,

,

,

,

;