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  Mathematics Assignments & Worksheets  For  Class IX Chapter-wise mathematics assignment for class 09. Important and useful extra questions strictly according to the CBSE syllabus and pattern with answer key CBSE Mathematics is a very good platform for the students and is contain the assignments for the students from 9 th  to 12 th  standard.  Here students can find very useful content which is very helpful to handle final examinations effectively.  For better understanding of the topic students should revise NCERT book with all examples and then start solving the chapter-wise assignments.  These assignments cover all the topics and are strictly according to the CBSE syllabus.  With the help of these assignments students can easily achieve the examination level and  can reach at the maximum height. Class 09 Mathematics    Assignment Case Study Based Questions Class IX 

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.

Note: 
  • Students of  IX standard learn all the formulas except Frustum of Cone.
  • Frustum of cone is only for the students of X standard.

  SOLID FIGURE CUBE

Curved Surface area of cube = 4(side)2

Total surface area of cube = (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

https://dinesh51.blogspot.com

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 =   

https://dinesh51.blogspot.com

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 = 

https://dinesh51.blogspot.com

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 


Note: This topic is only for the students of X standard

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

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

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

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


👉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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