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Maths Formulas Class 10 Ch-13 | Surface Area & Volume

Maths Formulas  Surface Area & Volume

Chapter 13 For Class IX & X

Surface Area and volume of Cube, Cuboid, Cylinder, Cone, Sphere, Hemi-Sphere, Frustum of Cone, Cylindrical Pipe, useful formulas for surface area and volume of solid figures 

Solid Geomatry

Everyday we have seen different materials and shapes in our surroundings. All that materials which we can touch and make use in our daily work are called solid figures.

These are also be called solid shapes because all these figures are involve three dimensions.

Further these are classified into different types. Main types are cube, cuboid, cylinder, cone, sphere, hemi-sphere and frustum of cone.

Here in this topic we discussed surface area and volume of these shapes.

  SOLID FIGURE CUBE

Curved Surface area of cube = 4(side)2

Total surface area of cube = 6(side)2

Volume of Cube = (side)3

 Diagonal of Cube = √3(side)2

Number of faces = 6

Number of vertices = 8

Number of Edges = 12

Each face of a cube is a square

 CUBOID

Curved Surface Area of cuboid = 2(l + b) ✖ h

Total Surface Area of cuboid = 2(lb + bh + hl)

Volume of cuboid = Length ✖ Breadth ✖ Height

Diagonal of  cuboid =   

Number of faces = 6  

Number of vertices = 8

Number of Edges = 12

Each face of a cube is a rectangle

CYLINDER

Curved Surface Area of cylinder = 2πrh

Total Surface Area of cylinder = 2πr(r + h)

Volume of cylinder = πr2h

Number of faces = 3 (One curved surface and two plane surface)

Number of vertices = 0

Number of edges = 2 

 CONE

Curved Surface Area = πrl

Total Surface Area = πr(r + l)

Volume =   

Number of faces = 2 (One curved surface and one plane surface)

Number of vertices = 1

Number of edges = 1

 SPHERE

Curved Surface Area = 4πr2

Total Surface Area =  4πr2

Volume = 

   

Number of faces = 1 (One curved surface ) 

Number of vertices = 0

Number of edges = 0

 HEMI-SPHERE


Curved Surface Area = 2
πr

Total Surface Area = 3πr2

Volume = 

Number of faces = 2 (One curved surface and one plane surface)

Number of vertices = 0

Number of edges = 1

 HOLLOW  CYLINDRICAL PIPE     

Inner Curved Surface Area = 2πrh
Outer Curved Surface Area = 2πRh
Area of two Rims = 2πR
2 - 2πr2
Total Surface Area = 2πrh + 2πRh + (2πR2 - 2πr2)

Volume = πh(R2 - 2πr2)
Number of faces = 4 (Inner and outer curved surface, top and bottom plane surface)
Number of vertices = 0
Number of edges = 4

 FRUSTUM OF  CONE (Deleted Topic)


Curved Surface Area = 
πl(r1 + r2)

Where,  

Total Surface Area = πl(r1 + r2) +   +  

Volume =  
Number of faces = 3 (One curved surface and two plane surface)

Number of vertices = 0

Number of edges = 2


Surface area and volumes

Solid Figure

Curved Surface Area

Total Surface Area

Volume

CUBE

 \[4\times \left ( side \right )^{2}\]

 \[6\times \left ( side \right )^{2}\]

 

\[\left ( side \right )^{3}\]

CUBOID

  \[2\left ( l+b \right )\times h\]

  \[2\left ( lb+bh+hl \right )\]

 

 \[lbh\]

CYLINDE

 \[2\pi rh\]

 \[2\pi rh+\pi r^{2}+\pi r^{2}\]\[=2\pi r\left ( r+h \right )\]

 

 \[\pi r^{2}h\]

CONE

 \[\pi rl\]

 \[\pi r\left ( r+l \right )\]

 

\[\frac{1}{3}\pi r^{2}h\]

SPHERE

 \[4\pi r^{2}\]

 \[4\pi r^{2}\]

  \[\frac{4}{3}\pi r^{3}\] 

HEMI - SPHERE

 \[2\pi r^{2}\]

 \[3\pi r^{2}\]

  \[\frac{2}{3}\pi r^{3}\]

FRUSTUM OF CONE(Deleted)

 \[\pi l\left ( r_{1}+r_{2} \right )\]

 \[\pi l\left ( r_{1}+r_{2} \right )+\pi r_{1}^{2}+\pi r_{2}^{2}\]

 \[\frac{1}{3}\pi h\left [ r_{1}^{2}+r_{2}^{2}+r_{1}r_{2} \right ]\]


👉While discussing surface area and volume unit conversion is an essential part. Without the knowledge of units students can not achieve the objective of the topic and they may face difficulty and mistakes most of the time. So in order to understand the techniques of unit conversion students click here

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