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Mathematical Formulars For College Students

Published on July 2016 | Categories: Types, Instruction manuals, Scrapbooking | Downloads: 72 | Comments: 0
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A Succinct description of over 20 Formulars on Goemetric. Formulars that capture the Area of Cones to Surface Area of Rhombus.

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Content

Mathematical
Formulas
For College
Students

GEOMETRIC
Shapes and Solids

1. SQUARE
Where 𝐋 is the Side and 𝐃 the Diagonal
Where 𝐩 perpendicular distance to it from opp. vertices
ο‚· Normal
𝐴𝑅𝐸𝐴 = 2(π₯ + 𝐛) × π‘
1 2
𝐴𝑅𝐸𝐴 = 𝑳 = 𝑫
2
2

𝑃𝐸𝑅𝐼𝑀𝐸𝑇𝐸𝑅 = πŸ’π‘³2 = 2𝑫2

ο‚· Quadrilateral
1
𝐴𝑅𝐸𝐴 = 𝐃(𝐩𝟏 + 𝐩𝟐 )
2

2. RECTANGLE
Where π₯ is the lenght, 𝐛 the breadth, and 𝐑 is height

ο‚· Normal Rectangle
𝐴𝑅𝐸𝐴 = π₯ × π›
𝑃𝐸𝑅𝐼𝑀𝐸𝑇𝐸𝑅 = 2(π₯ + 𝐛)
ο‚· 4 Walls of a Room
𝐴𝑅𝐸𝐴 = 2(π₯ + 𝐛) × π‘

3. TRIANGLE
ο‚· Normal Triangle
Where 𝐛 is the base and 𝐑 the height ,
𝐚, 𝐛, 𝐜 are the sides of the triangle,
𝐬 is the semi − perimeter of the triangle.
1
𝐴𝑅𝐸𝐴 = 𝐛𝐑 =
2

𝐬 𝐬 − 𝐚 𝐬 − 𝐛 (𝐬 − 𝐜)

𝑃𝐸𝑅𝐼𝑀𝐸𝑇𝐸𝑅 = 𝒂 + 𝒃 + 𝒄 = 2𝒔
ο‚· Isoceles Triangle
𝒃
𝐴𝑅𝐸𝐴 =
πŸ’πšπŸ − 𝐛 𝟐
4
𝑃𝐸𝑅𝐼𝑀𝐸𝑇𝐸𝑅 = 2𝒂 + 𝒃
1
𝐻𝑒𝑖𝑔𝑕𝑑 (𝒉) =
πŸ’πšπŸ − 𝐛 𝟐
2

4. POLYGON
ο‚· Regular
π΄π‘Ÿπ‘’π‘Ž π‘œπ‘“ 𝐻𝑒π‘₯π‘Žπ‘”π‘œπ‘› =

3 3 ÷ 2 × (𝑠𝑖𝑑𝑒𝑠)2

π΄π‘Ÿπ‘’π‘Ž π‘œπ‘“ π‘‚π‘π‘‘π‘Žπ‘”π‘œπ‘› = [2

2 + 1] × (𝑠𝑖𝑑𝑒𝑠)2

5. PARALLELOGRAM
Where 𝐛 is the base and 𝐚 slant ′diagonal′;
𝐑 is the corresponding attitude.

𝐴𝑅𝐸𝐴 = 𝐛𝐑
𝑃𝐸𝑅𝐼𝑀𝐸𝑇𝐸𝑅 = 𝟐𝐚 + πŸπ›

6. CIRCLE
Where 𝐫 is the radius, 𝐝 is diameter,
𝐜 is the circumference of the circle.

2
2
𝐝
𝒄
1
2
𝐴𝑅𝐸𝐴 = πœ‹π« = πœ‹
=
= (𝒄 × π«)
4
4πœ‹
2

𝑃𝐸𝑅𝐼𝑀𝐸𝑇𝐸𝑅 = 2πœ‹π« = Circumference of Circle

7. CIRCULAR SECTOR
Where 𝐫 is the radius, 𝐋 is the length of the sector.
𝐴𝑅𝐸𝐴 = πœ‹π« 𝟐
θ
𝑳 = πœ‹π«
180°

θ
360°

8. CIRCULAR RING
Where 𝐫 is the radius for inner circle,
𝐑 is the radius for outer circle.
𝐴𝑅𝐸𝐴 = πœ‹(𝑹2 − 𝐫 𝟐 )

9. ELLIPSE
Where 𝐫1 & 𝐫2 is the radius for 1st and 2nd circle.
𝐴𝑅𝐸𝐴 = πœ‹π«1 𝐫2

10.

TRAPEZOID/TRAPEZIUM

Where 𝐚 & 𝑏 are parrallel sides
Where 𝐜 & 𝑑 are slant sides
Where 𝐑 is the perpendicular distance
1
𝐴𝑅𝐸𝐴 = (𝒂 + 𝒃) × π’‰
2
𝑃𝐸𝑅𝐼𝑀𝐸𝑇𝐸𝑅 = 𝒂 + 𝒃 + 𝒄 + 𝒅

11.

RHOMBUS

Where 𝒅1 𝒅2 are diagonals, 𝐛 is the base
𝐑 is the height, 𝑺𝒅 𝑖𝑠 𝑠𝑖𝑑𝑒.
1
𝐴𝑅𝐸𝐴 = 𝒅1 𝒅2 = 𝒃 × π’‰
2
𝑃𝐸𝑅𝐼𝑀𝐸𝑇𝐸𝑅 = 4 × π‘Ίπ’… = 𝟐 (𝒅1 𝟐 + 𝒅2 𝟐 )
𝟏
𝑺𝒅 =
(𝒅1 𝟐 + 𝒅2 𝟐 ) = π‘Ίπ’Šπ’…π’† 𝒐𝒇 π‘Ήπ’‰π’π’Žπ’ƒπ’–π’”
𝟐

12.

SPHERE
Where 𝐫 is the radius
π‘†π‘’π‘Ÿπ‘“π‘Žπ‘π‘’ π΄π‘Ÿπ‘’π‘Ž = 4πœ‹π« 2
4πœ‹π« 3
π‘‰π‘œπ‘™π‘’π‘šπ‘’ =
3

13.

HEMISPHERE
Where 𝐫 is the radius

π‘‡π‘œπ‘‘π‘Žπ‘™ π‘†π‘’π‘Ÿπ‘“π‘Žπ‘π‘’ π΄π‘Ÿπ‘’π‘Ž = 3πœ‹π« 2
πΆπ‘’π‘Ÿπ‘£π‘’π‘‘ π‘†π‘’π‘Ÿπ‘“π‘Žπ‘π‘’ π΄π‘Ÿπ‘’π‘Ž = 2πœ‹π« 2
2

π‘‰π‘œπ‘™π‘’π‘šπ‘’ = πœ‹π« 3
3

14.

RECTANGULAR BOX
Where 𝐚, 𝐛, 𝐜 are the three sides of the Box.
π΄π‘Ÿπ‘’π‘Ž = πŸπ’‚π’ƒ + πŸπ’‚π’„ + πŸπ’ƒπ’„
π‘‰π‘œπ‘™π‘’π‘šπ‘’ = 𝒂𝒃𝒄

15.

CONE
Where 𝐫 is the radius (of the top), 𝐑 is the height
Where 𝐑 is the radius base of the frustum
Where π₯ is slant height of the frustum or cone .
Right Circular Cone
π΄π‘Ÿπ‘’π‘Ž = πœ‹π’“2 + πœ‹π’“π’
πΆπ‘’π‘Ÿπ‘£π‘’π‘‘ π‘†π‘’π‘“π‘Žπ‘π‘’ π΄π‘Ÿπ‘’π‘Ž = πœ‹π’“π’ = πœ‹π’“( 𝐑2 + 𝐫 2 )
π΄π‘Ÿπ‘’π‘Ž π‘œπ‘“ 𝑑𝑕𝑒 π‘π‘Žπ‘ π‘’ = πœ‹π’“2
π‘ π‘™π‘Žπ‘›π‘‘ 𝑕𝑒𝑖𝑔𝑕𝑑 π‘œπ‘“ π‘π‘œπ‘›π‘’ (π₯) = 𝐑2 + 𝐫 2
1

π‘‰π‘œπ‘™π‘’π‘šπ‘’ = πœ‹π’“2 𝒉
3

Frustum of a Cone
π΄π‘Ÿπ‘’π‘Ž = πœ‹[ 𝑹2 + 𝒓2 + 𝒍 𝑹 + 𝒓 ]
πΆπ‘’π‘Ÿπ‘£π‘’π‘‘ π‘†π‘’π‘“π‘Žπ‘π‘’ π΄π‘Ÿπ‘’π‘Ž = πœ‹(𝑹 + 𝒓)𝒍
π΄π‘Ÿπ‘’π‘Ž π‘œπ‘“ 𝑑𝑕𝑒 π‘π‘Žπ‘ π‘’ = πœ‹ 𝑹2 + 𝒓2
π‘†π‘™π‘Žπ‘›π‘‘ 𝑕𝑒𝑖𝑔𝑕𝑑 (π₯) =
1

𝐑2 + (𝐑 + 𝐫)2

π‘‰π‘œπ‘™π‘’π‘šπ‘’ = πœ‹π’‰(𝐫 2 + 𝒓𝑹 + 𝐑2 )
3

16.

CUBE
Where 𝒍 is the side of the cube
π΄π‘Ÿπ‘’π‘Ž = 6𝒍2
π‘‰π‘œπ‘™π‘’π‘šπ‘’ = 𝒍3

17.

CUBOID
Where 𝒍 is the side, 𝐛 is the base, and 𝐑 is the height
π΄π‘Ÿπ‘’π‘Ž = 2(𝒍𝒃 + 𝒃𝒉 + 𝒉𝒍)
π‘‰π‘œπ‘™π‘’π‘šπ‘’ = 𝒍 × π’ƒ × π’‰
π·π‘–π‘Žπ‘”π‘œπ‘›π‘Žπ‘™ =

18.

𝒍2 + 𝒃2 + 𝒉2

ELLIPSOID
Where 𝒓1 𝒓2 𝒓3 are the radii
4

π‘‰π‘œπ‘™π‘’π‘šπ‘’ = πœ‹π’“1 𝒓2 𝒓3
3

19.

CYLINDER
Where 𝒓 is radius and 𝐑 is the height
π΄π‘Ÿπ‘’π‘Ž = 2πœ‹π’“(𝒓 + 𝒉)
π‘‰π‘œπ‘™π‘’π‘šπ‘’ = πœ‹π’“πŸ 𝒉

πΆπ‘’π‘Ÿπ‘£π‘’π‘‘ π‘†π‘’π‘Ÿπ‘“π‘Žπ‘π‘’ π΄π‘Ÿπ‘’π‘Ž = 2πœ‹π’“π’‰
π΄π‘Ÿπ‘’π‘Ž π‘œπ‘“ 𝑑𝑕𝑒 2 π‘π‘–π‘Ÿπ‘π‘’π‘™π‘Žπ‘Ÿ 𝑒𝑛𝑑𝑠 = 2πœ‹π’“πŸ

20.

PRISM
Where 𝒃 is base, 𝐑 is the height and 𝒍 slant height
Where 𝒑 is the perimeter of the base
πΏπ‘Žπ‘‘π‘’π‘Ÿπ‘Žπ‘™ π΄π‘Ÿπ‘’π‘Ž = 𝒑 × π’‰
π‘‡π‘œπ‘‘π‘Žπ‘™ π΄π‘Ÿπ‘’π‘Ž = 2𝒃 + πΏπ‘Žπ‘‘π‘’π‘Ÿπ‘Žπ‘™ π΄π‘Ÿπ‘’π‘Ž

Irregular prism
π‘‰π‘œπ‘™π‘’π‘šπ‘’ = 𝒃𝒉𝒍

Rectangular prism
π‘‰π‘œπ‘™π‘’π‘šπ‘’ = 𝒂𝒃𝒄

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