[PDF] TNPSC – MATHS IMPORTANT FORMULAS

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TNPSC ² MATHS IMPORTANT FORMULAS

S.No Name of the

figure (ngah;)

Figure

(glk;)

Area (Sq. Units)

gug;gsT (r.myF)

Perimetre (P)

Rw;wsT

1. Triangle

Kf;Nfhzk;

1 2 x b x h AB + BC + CA 2.

Right triangle

Nrq;Nfhz

Kf;Nfhzk;

1 2 x b x h (base + height + hypotenuse) 3.

Equilateral

triangle rkgf;f

Kf;Nfhzk;

3 4 a2 where 3 = 1.732)

AB + BC + CA= 3A;

Altitude ,

h = 3 2 a units 4.

Isosceles

triangle ,U rkgf;f

Kf;Nfhzk;

h x 22ah

2a + 2

22ah
5.

Scalene

triangle (mrkgf;f

Kf;Nfhzk;)

( )( )( )s s a s b s c

Where a =

2 a b c

AB + BC + CA

= (a + b + c)

6. Quadrilateral

(ehw;fuk;) 1 2 x d x (h1 + h2) AB + BC + CD + DA

7. Parallelogram

(,izfuk;) b x h 2 x (a + b)

8. Rectangle

(nrt;tfk;) l x b 2 x (l + b)

9. Trapezium

(rhptfk;) 1 2 x h x (a + b) AB + BC + CD + DA

10. Rhombus

(rha;rJuk;) 1 2 x d1 x d2 where d1, d2 are diagonals (%iytpl;lk;) 4a

11. Square

a2 4a

Square (%iytpl;lk;) (d) (Diagonal length) =

2a No.

Name of the

figure figure

Surface

area tisgug;G Total surface area Volume 1.

Right circular

cylinder(Neh;tl;l jpz;k cUis)

2ʌrh 2ʌr(h + r) ʌr2h

2.

Right circular

hollow cylinder(Neh;tl;l cs;sPlw;w cUis)

2ʌh(R + r) 2ʌ(R + r)

(R ² r + h)

ʌR2h ² ʌr2h =

ʌh(R2 ² r2) =

ʌh(R + r)(R ² r)

3.

Right circular

cone (Neh;tl;l jpzkf; $k;G)

ʌrl ʌr(l + r)

21
3rh 4.

Frustum of a

cone (,ilf;fz;lk;)

221()3h R r Rr

5. Solid sphere

(jpz;kf;Nfhsk;)

4ʌr2 ______

34
3r 6.

Hollow Sphere

(cs;sPlw;w

Nfhsk;)

------- ______

334()3Rr

7. Solid hemisphere (jpz;k miuf;Nfhsk;)

2ʌr2 3ʌr2

32
3r 8.

Hollow

Hemisphere

(cs;sPlw;w miuf;Nfhsk;)

2ʌ(R2 + r2) 2ʌ(R2 + r2) +

ʌ(R2 - r2) =

ʌ(3R2 + r2)

gad;gLj;jg;gl;l cNyhfj;jpd; fd msT =

332(3Rr

9. tl;lf;Nfhzg;gFjp $k;ghf khw;wg;gLfpwJ tisgug;G = tl;lf;Nfhzg;gFjpapd; gug;G 2

360rl rSS u

tpy;ypd; ePsk;( l ) = $k;gpd; mbr;Rw;wsT(2ʌr) 10. Volume of water flows out through a pipe = (Cross section area x Speed x Time) Foha; topNa ghAk; jz;zPh; fd msT = (FWf;F ntl;Lg; gug;G X

Ntfk; X Neuk;)

11. No. of new solids obtained by recasting = Volumeof thesolidwhichismelted

Volumeof onesolidwhichismade

cUf;fp jahhpf;fg;gLk; Gjpa fd cUtq;fspd; vz;zpf;if cUffggll fd cUtjjpd fdmsT cUthffggll xU fd cUtjjpd fdmsT 12.

Conversions:

1 m3 = 1000 litres, 1 d.m3 = 1 litre, 1000 cm3 = 1 litre, 1000 litres = 1 kl

1 kP3 = 1000yp> 1nlrp kP3 = 1yp> 1000 nr.kP3 = 1yp> 1000yp = 1 fp.yp

CUBE (fdr;rJuq;fs;)

CUBIOD (fdr; nrt;tfk;)

‘ tl;lf;Nfhzg;gFjpapd; tpy;ypd; ePsk;

¾ xU tl;lf;Nfhzg;gFjpapd; ikaf;Nfhzk;

kw;Wk; Muk; r vdpy;> tpy;ypd; ePsk;

2360lrS u

myFfshFk;.

‘ tl;lf;Nfhzg;gFjpapd; gug;gsT

¾ xU tl;lf;Nfhzg;gFjpapd; ikaf;Nfhzk;

kw;Wk; Muk; r vdpy;> tl;lf;Nfhzg;gFjpapd; gug;gsT 2

360rSu

rJu myFfshFk;.

¾ tl;lf;Nfhzg;gFjpapd; gug;gsT =

2 lr rJu myFfs;

‘ tl;lf;Nfhzg;gFjpapd; Rw;wsT

¾ tpy;ypd; ePsk; l, tl;lf;Nfhzg;gFjpapd; Muk; r vdpy;> mjd; Rw;wsT

P=l + 2r myFfs;.

‘ Length of Arc

¾ If

is the central angle and r is the radius of a sector, then its arc length is given by

2360lrS u

units.

‘ Area of a Sector

¾ If

is the central angle and r is the radius of a sector, then the area of the sector is 2

360rSu

square units.

¾ Area of sector =

2 lr square units.

Key concept:

‘ Volume of a cube (fd msT )=

3a cubic units ‘ The Total surface area of a cube (T.S.A) (nkhj;jg;gug;G) 26a
square units. ‘ The Lateral surface area of a cube (L.S.A) (gf;fg;gug;G) 24a
square units. diagonal = 3a

‘ Volume of a cuboid

(fd msT )= l b h cubic units

‘ The Total surface area of a cuboid

(nkhj;jg; gug;G) =

2( )lb bh lh

sq.units.

‘ The Lateral surface area of a cuboid

(gf;fg;gug;G) =

2( )l b h

sq.units.

22( )( )a b a b a b

2 2 2( ) 2a b a b ab

2 2 2( ) 2a b a b ab

22( ) ( ) 4a b a b ab

3 3 2 2( ) ( )( )a b a b a ab b

3 3 2 2( ) ( )( )a b a b a ab b

3 3 3 2 2 3 3( ) 3 3 3 ( )a b a b a b ab a b ab a b

3 3 3 2 2 3 3( ) 3 3 3 ( )a b a b a b ab a b ab a b

2 2 2 2( ) 2( )a b c a b c ab bc ca

3 3 3 2 2 23 ( )( ) a b c abc a b c a b c ab bc ca

If a + b + c = 0 then

3 3 33 a b c abc

2( )( ) ( )x a x b x a b x ab

32( )( )( ) ( ) ( )x a x b x c x a b c x ab bc ca x abc

n(n+1)1 + 2 + 3 + ...... + n = 2 2

2LastNumber+11 3 5 ........ (2 1)2nn quotesdbs_dbs47.pdfusesText_47

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