Transcript Mensuration PPT - Recruitments Today

CUBE
Surface Area We will need to find
the surface area of the top, base and
sides.
a
Area of the top and bottom is
a
a
a
2a2
Area of sides (CSA) is 4a2
Therefore the formula is:
6a2
Volume V = a 3
Cuboid
Surface Area We will have to
calculate the area of sides, top
and base.
Area of sides = (CSA) is 2(lh+bh)
Area of top and base is 2(lb)
Therefore the formula is: 2(lb+lh+bh)
Volume v = lbh
TSA =
‫ת‬r(s+r)
2
CSA = 2πr
Surface Area We need to find the
outer surface area and the area of the
base.
Outer surface area (CSA) is 2 π r^2
Area of the base is π r^2
Therefore the formula is 3 π r^2
Volume V = πr^3
Surface Area of the model = CSA of cone +
CSA of cylinder = πrl + 2πrh
= π r ( l + 2h )
Surface Area of the
model = CSA of the
cylinder + CSA Of the
cone + Area of the
cylinder’s base
= 2πrh + πrl + πr2
= πr ( 2h + l + r )
Surface Area of the model =
CSA of hemisphere + CSA of
the cone
= 2πr2 + πrl
= πr ( 2r + l )
Surface area of the model = CSA of
the cylinder +
Surface area of the
sphere –
Area of the
cylinder’s base
= 2 πrh + 4 πr2 – πr2
= πr ( 2h – r ) + 4πr2
Surface area of the model = TSA of the the larger
cylinder + TSA of the smaller cylinder – Area of the
smaller cylinder’s base
= 2πRH + 2πR2 + 2πrh + 2πr2 – πr2
= 2πR ( H + R ) + 2πr ( h + r )
Surface area of the
model = CSA of the
cylinder + CSA of
both the cones
= 2πrh + 2πrl
= 2πr ( h + l )
Surface area of the model =
CSA of the cylinder
+ CSA of the
two hemispheres
= 2πrh + 2 ( 2πr2 )
= 2πrh + 4πr2
= 2πr ( h + 2r )
When two cubes are joined,
they form a cuboid.
In the given model when the
two cubes of side ‘a’ are joined,
we get a cuboid of dimension >
l = a + a
b = a
h = a
=
=
=
=
So the model’s surface area is
2 ( lb + bh +hl )
2 { ( a + a ) a + a2 + a ( a + a) }
2 ( 2a2 + a2 + 2a2 )
2 ( 5a2)
10a2
Surface area of the model = CSA of the cylinder +
CSA of the two hemispheres of the
same dimension
= 2πrh + 2πr2 + 2πr2
= 2πrh + 4πr2
= 2πr ( h + 2r
)
Surface area of the model =
TSA of the cuboid + CSA of the
hemisphere - CSA of the top of the
hemisphere
= 2 ( lb + hl + hb ) + 2πr2 – πr2
= 2 ( lb + hl + hb ) + πr2
Surface area of the model =
TSA of the cuboid + CSA of the
hemisphere - CSA of the top of the
hemisphere
= 2 ( lb + hl + hb ) + 2πr2 – πr2
= 2 ( lb + hl + hb ) + πr2
Surface area of the model =
CSA of the cylinder
+ CSA of the hemisphere
= 2πrh + 2πr2
= 2πr ( h + r )
•
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