surface area and volume 1
TRANSCRIPT
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SURFACE
AREA AND
VOLUMEProject work on
Mathematics
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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
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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
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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
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FINDING THE VOLUME OF CUBE :-
3a
aaa
a
a
a
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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
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FINDING TOTAL SURFACE AREA OF CUBOID:-
b
h
l
l
l
l
hhh
bb
b
)2(
)(2)(2)(2
)()()()()()(
hlbhlb
lhhbbl
lhhbbllhhbbl
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FINDING LATERAL SURFACE AREA OF CUBOID :-
hbl
hbhl
hbhbhlhl
)(2
)()(2
)()()()(
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FINDING VOLUME OF CUBOID:-
b
h
l
hbl
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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
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FINDING CURVED SURFACE AREA OF CYLINDER:-
h
r
rh2
hr 2Cylinder of area surface curved So
r 2r radius with circle ofperimeter know We
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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
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FINDING VOLUME OF CUBOID :-
h
r
hr
hr2
2
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CONE :- A surface generated by a straight line that moves along a closed curve while always passing through a fixed point.
h
r
l
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h
r
l
FINDING CURVED SURFACE AREA OF CONE :-
.
22
1
rl
rl
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h
r
l
FINDING TOTAL SURFACE AREA OF CONE :-
)(Area Surface Total
Area Surface Curved
circle of Area 2
rlr
rl
r
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h
r
l
FINDING VOLUME OF CONE :-
hr
hr
2
2
3
13
1
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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
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r
FINDING SURFACE AREA OF SPHERE :-
24 sphere of area surface So
circle a of area the times4 sphere of area Surface
r
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r
FINDING VOLUME OF SPHERE :-
3
3
3
43
4
r
r
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r
HEMISPHERE :- ‘Hemi’ also means ‘half’. So When Sphere is Divided into two equal parts Each equal part is called Hemisphere
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r
FINDING CURVED SURFACE AREA OF HEMISPHERE
2
2
2
r2
circle area thetwicehemisphere of area surface Curved
r
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r
TOTAL SURFACE AREA OF HEMISPHERE
2
2
3
r3
circle area theThriceHemisphere of area surface Total
r
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r
VOLUME OF HEMISPHERE
2
2
3
23
2
r
r