( a  + b ) ²  =  a²  +  b²   +  2ab

( a  - b ) ²  =  a²  +  b²   -  2ab

( a  + b ) ³  =  a³  +  b³   +  3a²b  +  3b²a                    

( a  - b ) ³  =  a³  -  b³   -  3a²b  +  3b²a

a³ -  b³       =   (a -  b)[ a²   +   b²  +  ab]

a³ +  b³       =   (a +  b)[ a²   +   b²  -  ab]

a² -  b²       =    (a +b) (a – b)

a² +  b²       =    (a +b)²   -  2ab

(a +  b + c)² =  a²  +  b² + c² + 2ab  + 2bc + 2ca

a^m.aⁿ =  a^{m + n}

Area of circle  =    πr²  ,    where r is the radius of the circle

Acute angle :-   Acute angle are those angle which are less than 90°                    

Obtuse angle :-  obtuse angle are those angle which are greater than 90°

 Rectangle:-        Area :  Length x breadth        Perimeter :  2(length + breadth)

Square :-             Area :  (side)²                        Perimeter :   4(side)

Name of the solid

Lateral/Curved surface area

Total surface area

Volume

Cuboid

2h(l + b )

2(lb  + bh  + hl)

lbh

Cube

4a²

6a²

a³

Right Circular cylinder

2πrh

2πr(h + r )

π r²h

Right Circular cone

π rl

π r(l + r )

1/3 πr²h

Sphere

4 πr²

4 πr²

4/3 πr³

Hemisphere

2 πr²

3 πr²

2/3 πr³

Where    r : radius         h: height      l: Slant height