SURFACE

AREA AND

VOLUMEProject work on

Mathematics

CUBE :- A solid three-dimensional geometric figure bounded by six planes; each of the six sides or faces of a cube is a

a1

a2

a3

321 aaa

FINDING THE SURFACE AREA OF CUBE.

a

a

aa

a

a

a

a

a

26a

a)6(a

a)(aa)(aa)(aa)(aa)(aa) (a

a

aa

FINDING LATERAL SURFACE AREA OF CUBE:-

2222

2

4)aa(6a

-:area remaining

So reduced. is bottom and topof area The

.6acube of area surface l that totaknow We

a

FINDING THE VOLUME OF CUBE :-

3a

aaa

a

a

a

CUBOID :- A three-dimensional geometric figure formed of six rectangular plane faces, each set at right angles to the four sides adjacent to it.

b

h

l

FINDING TOTAL SURFACE AREA OF CUBOID:-

b

h

l

l

l

l

hhh

bb

b

)2(

)(2)(2)(2

)()()()()()(

hlbhlb

lhhbbl

lhhbbllhhbbl

FINDING LATERAL SURFACE AREA OF CUBOID :-

hbl

hbhl

hbhbhlhl

)(2

)()(2

)()()()(

FINDING VOLUME OF CUBOID:-

b

h

l

hbl

CYLINDER:- Cylinder consists of two circular bases of equal area in parallel planes, that are connected by a lateral surface that intersects the boundaries of the bases.

h

r

FINDING CURVED SURFACE AREA OF CYLINDER:-

h

r

rh2

hr 2Cylinder of area surface curved So

r 2r radius with circle ofperimeter know We

TOTAL SURFACE AREA OF CUBOID :-

h

r

)(2

22cuboid of area surface Total

2 circles twoof Area

2 cuboid of area surface Curved

2

2

hrr

rrh

r

rh

FINDING VOLUME OF CUBOID :-

h

r

hr

hr2

2

CONE :- A surface generated by a straight line that moves along a closed curve while always passing through a fixed point.

h

r

l

h

r

l

FINDING CURVED SURFACE AREA OF CONE :-

.

22

1

rl

rl

h

r

l

FINDING TOTAL SURFACE AREA OF CONE :-

)(Area Surface Total

Area Surface Curved

circle of Area 2

rlr

rl

r

h

r

l

FINDING VOLUME OF CONE :-

hr

hr

2

2

3

13

1

SPHERE :- Surface of which every point is the same distance from a

fixed point known as the centre. From every aspect it has the same appearance. A sphere may be described by the rotation of a semicircle or circle, about its

diameter.

r

r

FINDING SURFACE AREA OF SPHERE :-

24 sphere of area surface So

circle a of area the times4 sphere of area Surface

r

r

FINDING VOLUME OF SPHERE :-

3

3

3

43

4

r

r

r

HEMISPHERE :- ‘Hemi’ also means ‘half’. So When Sphere is Divided into two equal parts Each equal part is called Hemisphere

r

FINDING CURVED SURFACE AREA OF HEMISPHERE

2

2

2

r2

circle area thetwicehemisphere of area surface Curved

r

r

TOTAL SURFACE AREA OF HEMISPHERE

2

2

3

r3

circle area theThriceHemisphere of area surface Total

r

r

VOLUME OF HEMISPHERE

2

2

3

23

2

r

r