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Math Formulas | Cylinder

Smart Math Formula, A cylinder is a solid bounded by a cylindrical surface and two parallel planes. 

Volume of Cylinder = πr²h
Curved Surface Area of Cylinder = 2πrh
Total Surface Area of Cylinder = 2πr [ h + r ]

Note :
        r = radius, h = height


Example

Question : Find the volume, curved surface and total surface area of a cylinder with the given radius 3 and height 4.

 Answer : Find the volume.
            Volume = πr²h = 3.14 . 3² . 4 = 3.14 . 9 . 4 = 113.04 .
 

Answer : Find the curved surface area.
             = 2πrh = 2 x 3.14 x 3 x 4 = 75.36.
 

Answer : Find the total surface area.
             = 2πr [h + r] = 2 . 3.14 . 3[4 + 3] = 6.28 x 3[7] = 6.28 x 21 = 131.88.

That is example will clearly illustrates how to calculate the Volume, Curved Surface and Total Surface Area of a Cylinder manually, this Smart Math Formula Cylinder.



Math Formulas | Rectangular box (Beams)

Smart Formula Math  Rectangular box (Beams) is Cube and the beam is not really much different. If the cube all the sides the same length of the beam are not all the same length. 

Volume = l x w x h [in fact equal to the cube, it's just that the cube has all the ribs of the same length].
Beam Surface Area = 2 . {[l . w]+[l . h]+[w . h)]
Roving Beams = 4 . [l + w + h]
The roots of the diagonal spaces = [ l squared + w squared + h squared ]



Note :
length = l , width = w , height = h

Example

Question :
Find the Volume and  Surface Area beam below if length =4,width =3, high= 5

Answer :
Volume Of beams = l x w x h = 4 x 3 x 5 = 60

Beam Surface Area = 2 x {(l x w) + (l x h) + (w x h)}
2 x {(4 x 3) + (4 x 5) + (3 x 5)} = 2 x ( 12 + 20 + 15 ) = 94

That is example find the volume and area of beams which was submitted by the smart math basic formula.



Math Formulas | Pentagonal Pyramid

FormulaMath
Formula Math Of Pentagonal Pyramid
Area of Base [ A ]= [ 5/2 ]a.s
Surface Area of Pyramid = [ 5/2 ]a.s + [ 5/2]s.l = A + [ 5/2 ]s.l
Volume of Pyramid = [ 5/6 ]a.b.h

Note :
s = side, h = height , l = length, 

a = apothem ,b = lant height


Example


Question : Find the surface area and volume of a pentagonal pyramid with the given apothem length 2, side 3, height 4 and the slant height 5.

Answer : Find the area of the base.
Solution : Area of the base [A] = [ 5/2 ]a.s = 5/2 . 2 . 3 = 15.

Answer :  Find the surface area of pyramid.
Solution : Surface Area of Pyramid = A + [ 5/2 ]s.l = 15 + [5/2] .3 . 5) = 15 + [5/2 x 15] = 15 + 37.5 = 52.5.

Answer : Find the volume of pyramid.
Solution :Volume of Pyramid = [ 5/6 ].a.b.h = [5/6] . 2 . 3 x 4 = (0.833) . 24 = 20.

That is  example will clearly how to calculate the Volume by Formula Math Surface Area of a Pentagonal Pyramid.

Math Formulas | Hexagonal Pyramid



A Hexagonal Pyramid is a pyramid with a Hexagonal base.

Area of Base [ A ] = [6/2]a.s = 3.a.s
 
Surface Area of Pyramid 
= 3.a.s + 3.s.l = A + 3.s.l
 
Volume of Pyramid = a.b.h 


Note :
a = apothem,
l =  length,  b = side, 
h = height and s = slant height


Example

Formula Math Smart Hexagonal Pyramid Example :
Question : Find the surface area and volume of a hexagonal pyramid with the given apothem length 2, side 3, height 4 and the slant height 5.

Answer : Find the area of the base.
Area of the base [ A ] = 3as = 3 x 2 x 3 = 18.

Answer : Find the surface area of pyramid.
Surface Area of Pyramid = A + 3sl = 18 + [3 . 3 .5] = 18 + 45 = 63.

Answer : Find the volume of pyramid.
Volume of Pyramid = a.b.h = 2 . 3 . 4 = 24.

That is example will clearly illustrates how to calculate the Volume, Surface Area of a Formula Math Smart Hexagonal Pyramid .

Math Formulas | Cone

Smart Math Formula, A cone is a three-dimensional geometric shape consisting of all line segments joining a single point to every point of a two-dimensional figure.

Slant height of Cone 
[ l ] = Sqrt [r² + h²]
 

Volume of Cone = [1/3] πr²h

Curved Surface Area [ CSA ] of Cone = πrl
Total Surface Area [ TSA ] of Cone = πr [ l + r ]


Note :
r = radius, l = slant height, h = height


Example 

Question : Find the volume, curved surface and total surface area of a cone with the given radius 3 and height 4.

Answer : Find the slant height.
Slant height [ l ] = Sqrt [r² + h²] = Sqrt [3² + 4²]= Sqrt [9 + 16]
=Sqrt [25] = 5.

Answer : Find the volume.
Volume = [1/3]πr²h = [1/3] x 3.14 x 3² x 4 = 0.33 x 113.04 = 37.68.

Answer : Find the curved surface area [ CSA ].
CSA = πrl = 3.14 x 3 x 5 = 47.1.

Answer : Find the total surface area [ TSA ].
TSA = πr [l + r] = 3.14 x 3[5 + 3] = 3.14 x 3(8) = 3.14 x 24 = 75.36.

That is example will clearly illustrates how to calculate the Volume, Curved Surface and Total Surface Area of a Smart Math Formula Cone.

Math Formulas | Volum Of Cube

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Smart Math Formula, A cube has a three-dimensional solid object bounded by six square faces, facets or sides, with three meeting at each vertex.

Cube Math Formula :
Volume of Cube = s³

                         Side of Cube     = ³√v
                         Surface Area of Cube = 6s²
Note :
s = side
                                             

Example

Question : Find the volume, surface area and side of a cube with the given side 5.

Answer : Find the volume.
Volume = s³ = 5³ = 125.

Answer : Find the surface area.
Surface Area = 6.s² = 6 . 5² = 6 . 25 = 150.

Answer : Find the Side.
s=³√v = ³√125 = 5


That smart formula cube example will clearly illustrates how to calculate the Volume, Surface Area and Side of a Cube.