Surface Area of Prism and Cylinder

Surface Area of Prism and Cylinder
Grade 6
Warm Up
Q1. Draw a top and a front view of each figure.
1.
2.
2
Warm Up
Make a perspective drawing of each figure by
using the top , side and front views as shown.
3.
4.
3
Warm Up
Make a perspective drawing of each figure by
using the top , side and front views as shown.
5.
4
Let Us Review
3D figures are figures which have length, width
and height.
A cone has only one face, one vertex and has no
edges.
A cube has six faces, 8 vertices and 12 edges.
A cylinder has 2 faces, 0 vertices and 0 edges.
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Let Us Review
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A square pyramid has 5 faces , 5 vertices and 8
edges.
A rectangular Prism has 6 faces, 8 vertices and
12 edges.
A sphere has no face, no vertex and no edges.
Lets get started
Surface Area:
The surface area of a three-dimensional
figure is the sum of the areas of all its faces.
Prism:
A prism is a polyhedron consisting of two
parallel, congruent faces called bases.
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Examples of prism
Triangle Prism
Pentagonal Prism
Rectangular Prism
Hexagonal Prism
Octagonal Prism
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Figures of prisms
Triangular prism
Note: A prism is named according to the shape of its
base.
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Edges and vertices
Solid figure
Number of
faces
Number of
edges
Number of
vertices
Triangular
prism
5
9
6
Rectangular
prism
6
12
8
Pentagonal
prism
7
15
10
Hexagonal
prism
8
18
12
Octagonal
prism
10
24
16
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Surface Area of Rectangular prisms
A rectangular prism has 2 ends and 4 sides. Opposite
sides have the same area. The surface area is the sum of
the areas of all six sides.
To find the surface area of Rectangular Prisms:
Find the area of two sides (Length*Height)*2 sides
•Find the area of adjacent sides (Width*Height)*2 sides
•Find the area of ends (Length*Width)*2 ends
•Add the three areas together to find the surface area
Surface Area of Rectangular prism = 2·L·W + 2·L·H + 2·W·H
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Example
Find the surface area of a rectangular prism with 5 cm
long, 3 cm wide and 2 cm. high
Solution:Surface Area of Rectangular prism = 2·L·W + 2·L·H + 2·W·H
=2.5.3+2.5.2+2.3.2
=30 + 20 + 12
= 62 cm2
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Formula for Surface Area of
prisms
Triangular prism:
Triangle with base 'b', height 'h', and sides S1, S2
and S3. Surface area = bh + (S1+ S2 + S3)h
Regular Pentagonal prism:
Surface Area = 5as + 5sh , where a denotes
apothem length, s = side length and h = height.
NOTE: Surface Area of any prism =Lateral area +
Area of two ends
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Cylinder
To find the surface area of a cylinder add the
surface area of each end plus the surface area of
the side.
Surface area of each end = πr2.
There are two ends so their combined surface area
is 2*πr2.
Surface area of the side = circumference times the
height or 2πrh.
The entire formula for the surface area of a
cylinder is 2*πr2 + 2πrh
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Figures of cylinder
r
h
hi
of s th
th e h
r i e c eig
st
yli
ht
h
n
of e r der
th adi
e t us ,
op
Surface area of a cylinder = 2*πr2 + 2πrh
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Example
Find the Surface Area of cylinder with a height of
5 cm and radius of 2 cm.
Surface area of a cylinder = 2*πr2 + 2πrh
= 2*π 22 + 2π(2)(5)
= 8π + 20 π
= 28 π cm2
where π = 3.14
= 28 * 3.14 cm2
= 87.92 cm2
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Lets take a break!!
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Your Turn
1) A rectangular Prism has ___ edges.
2) _________ is a polyhedron.
3) __________ is the sum of the areas of all its faces.
4) Write examples of prisms.
5) A prism is named according to the shape of its ______.
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Your Turn
6) Surface Area of Rectangular prism _________.
7) Surface Area of cylinder __________.
8) Surface Area of a prism = __________ + _________.
9) How many faces in pentagonal prism?
10) Write the number of vertices in octagonal prism.
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1) Find the base area of the right rectangular prism.
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2) The surface area of the cylinder is 2136.56
cm2, radius is 17cm. Find the height. (π =3.14)
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3) Find the surface area of a hexagonal prism with a
height of 6 ft, the length of each side of its hexagonal
base is 3 ft and a 2.6 ft radius.
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Lets review what we have learned
in our lesson
Surface Area of a Prism
The surface area of a prism is the sum of the areas of
all the sides of the prism. The formula for the surface
area of a prism therefore depends on the type of prism.
Surface Area of a Cylinder
The surface area of a cylinder is the sum of the areas
of the two bases and the lateral face of the cylinder.
surface area of a cylinder = 2*π
πr2 + 2π
πrh
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Types of prism
The name of a prism depends upon its base polygons.
If the bases are triangles, then it is a TRIANGULAR prism.
A RECTANGULAR prism has bases which are rectangles .
The other types of prisms are pentagonal prism, hexagonal prism
and octagonal prism.
Surface Area of prism:
Surface Area of any prism = Lateral area + Area of two ends
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You did great in your lesson today !
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