For more free Video / Audio Tutorials & Study Material visit - www.ssc-cgl2014.in And for regular updates on our website like us on facebook - www.facebook.com/cgl.ssc2014 Two-dimensional figures
Three-dimensional figures
Circle - common
Sector of a Circle
All pdntl on the c1rcumference of c clrcl.
1M pil-'lhapIcI pfece of a cIrcle 'OJ' out' by hto radii.
A-
D-2R
D-2R
1=2nR=lrD ..2 lW2 A=11X=T
1=211R=11D
..nlch ore tongnJenl
V=A·ff
14
cnd aewral trion4)Ul0l"101.. 01 teen.
1
S=Add the arlO of the ~ to the sum of the areaJ of oflof the trio •• Joc:es
A-Area of bcse P-Perimeter of 1>0..
-c
P=2(a.+b) A=a.·h
~+-4-2(a.2+-b2) A=a.b·sina.
P-Porinct.
A-hoa
A ",_tord
art. equ
w
odjac.. t
with two palro of dl,tlnct
V-Vofume
s-Serfoco.....
Sphere
w w
"",os and 3 ,ides. A tri~e ,ith aI three ,;des of equal length,
R=~
......
A hrniapner. Is nolf Q sphere, .Ith cirallar foee and Q'le bowI-"aped
one flat face.
Cylinder
S=211rH+21r r V=1rff(R2-
"C
rJ
R
Il--
Heq.1
R.r-Rodius
of bose
V-Vd.... S-SJrfuce area
with one ri~t a"'ll.,
P-a.+b+c c=v;JHl
A-1V4lf-a.'
A~
P-Porlmet ..
P- Perlmet.. A- Area
V=11r2ff S=2 11r2-t2 IT rh
Right Triangle
P-a.+-2b A-!b20sino
A-Anoo
ff- Height p',Jt-Perimeltr of
1- sront heighl V- Volume S- Surroce area
S-s...roc. area
A=sJV3
A ~.
,
r- RadIus of DoH
P-Primet"
two ,ld.1 ot equal 1"91h.
I
'\..4,-......of b...
V-Vdumo
r-
R= 2r
A. trlong, 'lri'th
S=¥p,+-~)'I V,(A,+A,+-'iAA)'H
S=<411r2 V-V.ume RadIus of ba_ S-Surf, .. area
r=~
Isosceles Triangle
~
c)f(ndtf" Is CI loUd toot 11C11two parallel facet which ore concruenl elrcles.The line connecting Rff+-2(1rJ#.1r.,J) the c:e'lters of tho bu. r, CCllle
P=3a.
A-Ar ..
Frustumof a Pyramid 1hf portion of a p)I'amld that II.. bel, .. n tho boaI and (I plane cutting through It porallel to Ih,I>o .. ,
V=j 1rrJ
Hollow cylinder
Triangle - common Equilateral Triangle
A= Vs(s-a.)(s-b)(s-c)
1- the .Ionl llelif' ff-Helif'1 V-Volume
Hemisphere
A 89here i, a lOUd in which Gil the pdnts on the round surface ore equidistant from 0 fiJI:ed point, known as the centre of the tph...
Kite
on. polr
of parallel Ildtl
pQ)IjCn (pIa,.. ~~re) "th 3
A p)I"OmldI. , I(jld with 0 poI)9OOCII _
gl
A quocriloterol with opposite sides parallel.
Trapezoid A quod,notro! elth at ltalt
R,R,-
V=lA·ff
sc
rt,~4-4a.2
~ Totol turlOct ortcJ V-Ydwne S-Surfllce area 1- the slant htf911 RadiUSof bo...
Pyramid
A=a.b A-1d2 P=2·(a.+b)
Parallelogram
P=4·a. A=a.h A=-a.· *sinu A="i
,
bo.. S- SiJrfoce erec
P- Perinet.,. A-Ana
A pclrall elOC)"am with all sides equal
P- Perimeter A- Areo
~
O-Helghl r- Radius of
or.
D
top.
V=~ 11r20 S= 11 rl.+-1f r2
A quodttat .. aI .ith adjacent perpendIcular (01 four 1Il•• f"" rl~t a"'lln),
ongl'cl....
Frustum of a Right Circular Cone
t_..
-s-
A-hOG
b
Rhombus
V-Vdume
2
.s
P- Perimeter A- Ar ec
V-Volume
20
A=a.2 A=fd2 P=4·a. d=a.~
A- Areo of base P- Prlmeter of bcse
A cone is 0 !IOIid with 0 cirt:ulor bese, II has a CIlMd ,.,rfacewhich le, decrtotel h l1ze) to 0 wrta: ot the
Rectangle
oppOlit. ,ld •• parallel.
P- Perimeteraf DoH
I=Ra.~
Square A quadrllaterol wIth
A-Ar .. af_
Cone
curwd portKn of a circle.
A
if" <180
Areo
A=P*ff
V=A'ff
Arc of a Circle
Either of the two regi(J1s into .mien 'lhfc:h a secant or a chord alts 0 efrcle
A-
tndl
A=11R1¥
Segment of a Circle
A=Ma.-A_ if a.>180 11K A=360Q +-A...,
ot both
2
A-Ana
Ar ee
pd)9m1
.in
ore equIdIstant from III center.
Rectangular Parallelepiped
Prism A prl,", I. a ,.;~ lhol hot lwo po'alol _
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ff-Height r-- Radius of bose
V-VoIume
S-Surfoce eree
