Surface area and volume formulas
INTRODUCTION :
The term territory with regards to looking over alludes to the zone of a lot of land anticipated upon the level plane, and not to the genuine region of the land surface.
Territory might be communicated units -
1 Square meters
2 Hectares (1 hectare = 10,000 m2)
3 Square feet
4 Area (1 section of land = 4840 sq. yd. = 43.560 sq. ft.)
Territory might be communicated units -
1 Square meters
2 Hectares (1 hectare = 10,000 m2)
3 Square feet
4 Area (1 section of land = 4840 sq. yd. = 43.560 sq. ft.)
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| area formula |
Computation of area and volume
The main goal of this study is to calculate the areas and volumes.
Typically the terrains will consist of polygons, with varying shapes.
There are formulas for regular polygons such as triangles, squares, rectangles and other common shapes.
However when it comes to determining the areas of polygons various methods are employed.
Earthwork calculation involves tasks like excavating channels digging tunnels for laying pipelines designing embankments and earthen dams constructing farm ponds and leveling land. In calculations the cross sectional areas at intervals along the length of the channels and embankments are initially determined. Then the volume, between cross sections is calculated using either trapezoidal or prismoidal formulas.
Area calculation can be performed using any of the following methods;
a) Mid method
b) ordinate method
c) Trapezoidal rule
d) Simpsons rule
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| Computation of area and volume |
Formula for geometrical figures
Perimeter Formula :
| Square | 4 × side |
| Rectangle | 2 × (length + width) |
| Parallelogram | 2 × (side1 + side2) |
| Triangle | side1 + side2 + side3 |
| Regular n-polygon | n × side |
| Trapezoid | height × (base1 + base2) / 2 |
| Trapezoid | base1 + base2 + height × [csc(theta1) + csc(theta2)] |
| Circle | 2 × pi × radius |
| Ellipse | 4 × radius1 × E(k,pi/2) E(k,pi/2) is the Complete |
side2
Square shape
length × width
Parallelogram
base × tallness
Triangle
base × tallness/2
Normal n-polygon
(1/4) × n × side2 × cot(pi/n)
Trapezoid
tallness × (base1 + base2)/2
Circle
pi × radius2
Oval
pi × radius1 × radius2
3D square (surface)
6 × side2
Circle (surface)
4 × pi × radius2
Chamber (surface of side)
border of circle × stature
2 × pi × sweep × stature
Chamber (entire surface)
Regions of top and base circles + Area of the side
2(pi × radius2) + 2 × pi × sweep × stature
Cone (surface)
pi × sweep × side
Torus (surface)
pi2 × (radius22 - radius12)
Calculating the surface area and volume of a sphere is based on its radius (r) which's the distance, from the center to any point on the spheres edge. The formulas for surface area and volume are straightforward to remember. Like calculating the circumference of a circle you use pi (π) which can be approximated as either 3.14 or 3.14159 (commonly accepted as 22/7).
- Surface Area = 4πr2
- Volume = 4/3 πr3
Surface Area and Volume of a Cone
Now lets move on to discussing cones which're pyramid shaped structures, with a base and slanting sides that converge at a single point. To determine their surface area or volume you need to know the base radius and side length.
- s = √(r2 + h2)
With that, you can then find the total surface area, which is the sum of the area of the base and area of the side.
- Area of Base: πr2
- Area of Side: πrs
- Total Surface Area = πr2 + πrs
To find the volume of a sphere, you only need the radius and the height.
- Volume = 1/3 πr2h
Area & Volume Calculations Watch -
1 In the trapezoidal formula the line
joining the top of the ordinates is assumed
= straight
2 In Simpson’s formula the line joining the top of the
ordinates is considered
= parabolic
3 In Simpson’s formula the number of ordinates must be
= odd
4 In the trapezoidal formula the of
divisions should be
= either odd or even
5 Irregular area may be computed by an
instrument known as
= planimeter
6 When the tracing point is moved
along a circle without rotation of the wheel then the circle is
= zero circle
7 when the anchor point is inside the
figure the area of the zero circle is
= added
8 The value of the planimeter constant
C is added only when
= the anchor point is inside the
figure
9 The volume computed by the
prismoidal method is considerd
= exact
10 To obtain the correct volume using
the trapezoidal rule the prismoidal correction
= subtracted
11 The horizontal distance through the
excavated earth transported from the borrowpit
= lead
12 The vertical distance through which
excavated earth is lifted is
= lift
13 The graph prepared in order to
facilitate proper distribution of excavated earth is
= mass diagram
14 With notations carrying their usual
meanings the cross-sectional area of an embankment is
= (b+sh)h
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Chain Surveying Note - Read
Compass Traversing Note - Read
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