Dictionary Rank of a Word | Permutations & Combinations

 PERMUTATIONS & COMBINATIONS Rank of the word or Dictionary order of the English words like COMPUTER, COLLEGE, SUCCESS, SOCCER, RAIN, FATHER, etc. Dictionary Rank of a Word Method of finding the Rank (Dictionary Order) of the word  “R A I N” Given word: R A I N Total letters = 4 Letters in alphabetical order: A, I, N, R No. of words formed starting with A = 3! = 6 No. of words formed starting with I = 3! = 6 No. of words formed starting with N = 3! = 6 After N there is R which is required R ----- Required A ---- Required I ---- Required N ---- Required RAIN ----- 1 word   RANK OF THE WORD “R A I N” A….. = 3! = 6 I……. = 3! = 6 N….. = 3! = 6 R…A…I…N = 1 word 6 6 6 1 TOTAL 19 Rank of “R A I N” is 19 Method of finding the Rank (Dictionary Order) of the word  “F A T H E R” Given word is :  "F A T H E R" In alphabetical order: A, E, F, H, R, T Words beginni

Surface area and volume (Solid shapes)

Surface area and volume  (Solid shapes) Chapter 13 Class X

Interactive 3d shape, formulas volume and surface area, surface area and volume formulas class 9th and 10th , 3d shape formulas volume and surface area for class 9th, 

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.


\[Curved Surface Area=4(side)^{2}\]

\[Total Surface Area=6(side)^{2}\]

\[Volume = (Side)^{3}\]


\[Curved Surface Area = 2(l+b)\times h\]

\[Total Surface Area = 2(lb+bh+hl)\]

Volume = Length X Breadth X Height


\[Curved Surface Area = 2\pi rh\]

\[Total Surface Area = 2\pi r\left ( r+h \right )\]

\[Volume=\pi r^{2}h\]



\[Curved\: Surface\: Area\\=\pi rl\: \: where\:\: l=\sqrt{h^{2}+r^{2}}\]

\[Total\; Surface\; Area=\pi r\left ( r+l \right )\]

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



\[Curved\; Surface\; Area=\: 4\pi r^{2}\]

\[Total\; Surface\; Area=\: 4\pi r^{2}\]

\[Volume=\: \frac{4}{3}\pi r^{3}\]


\[Curved\; Surface\; Area=2\pi r^{2}\]

\[Total\; Surface\; Area=3\pi r^{2}\]

\[Volume=\frac{2}{3}\pi r^{3}\]



\[Inner\; Curved\; Surface\; Area=2\pi rh\]

\[Outer\; Curved\; Surface\; Area=2\pi Rh\]

\[Area\; of\; Two\; Rims=2\pi \left ( R^{2}-r^{2} \right )\]

\[Total\; Surface\; Area\\=\pi R^{2}h+\pi r^{2}h+2\pi \left ( R^{2}-r^{2} \right )\]

\[Volume=\pi h\left ( R^{2}-r^{2} \right )\]


\[Curved\; Surface\; Area=\pi l\left ( r_{1}+r_{2} \right ) \\ where\, \, l=\sqrt{h^{2}+\left ( r_{1}-r_{2}\right )^{2}}\]

\[Total\; Surface\; Area\\=\pi l\left ( r_{1}+r_{2} \right )+\pi r_{1}^{2}+\pi r_{2}^{2} \\ \, \, l=\sqrt{h^{2}+\left ( r_{1}-r_{2}\right )^{2}}\]

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

Surface area and volumes

Solid Figure

Curved Surface Area

Total Surface Area



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

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


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


  \[2\left ( l+b \right )\times h\]

  \[2\left ( lb+bh+hl \right )\]




 \[2\pi rh\]

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


 \[\pi r^{2}h\]


 \[\pi rl\]

 \[\pi r\left ( r+l \right )\]


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


 \[4\pi r^{2}\]

 \[4\pi r^{2}\]

  \[\frac{4}{3}\pi r^{3}\] 


 \[2\pi r^{2}\]

 \[3\pi r^{2}\]

  \[\frac{2}{3}\pi r^{3}\]


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

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

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

๐Ÿ‘‰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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