1. Surface Area of Prism and Cylinder
Our Lesson
Surface Area of Prism and Cylinder

2. Warm Up Q1. Draw a top and a front view of each figure. 1. 2.
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3. Warm Up
Make a perspective drawing of each figure by using the top , side and front views as shown. 3. 4.
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4. Warm Up
Make a perspective drawing of each figure by using the top , side and front views as shown. 5.
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5. 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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6. Let Us Review 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.
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7. 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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8. Examples of prism Triangle Prism Rectangular Prism Pentagonal Prism
Hexagonal Prism
Octagonal Prism
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9. Figures of prisms
Triangular prism
Note: A prism is named according to the shape of its base.
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10. Edges and vertices Solid figure Number of faces Number of edges
Number of vertices
Triangular prism 5 9 6
Rectangular prism 12 8
Pentagonal prism 7 15 10
Hexagonal prism 18
Octagonal prism 24 16
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11. 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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12. 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 = =
= 62 cm2
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13. 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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14. 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 = r2.
There are two ends so their combined surface area is 2*r2.
Surface area of the side = circumference times the height or 2rh.
The entire formula for the surface area of a cylinder is 2*r2 + 2rh
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15. h is the height of the cylinder, r is the radius of the top
Figures of cylinder
h is the height of the cylinder, r is the radius of the top h r
Surface area of a cylinder = 2*r2 + 2rh
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16. Example
Find the Surface Area of cylinder with a height of 5 cm and radius of 2 cm.
Surface area of a cylinder = 2*r2 + 2rh
= 2* (2)(5)
= 8 + 20 
= 28  cm2
where  = = 28 * 3.14 cm2
= cm2
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17. Your Turn A rectangular Prism has ___ edges. 12
_________ is a polyhedron. Prism
__________ is the sum of the areas of all its faces. Surface Area
Write examples of prisms. Triangular prism, Rectangular, Pentagonal, hexagonal, octagonal
A prism is named according to the shape of its ______. base
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18. Your Turn
6) Surface Area of Rectangular prism _________. 2·L·W  +  2·L·H  +  2·W·H
7) Surface Area of cylinder __________.
2*r2 + 2rh
8) Surface Area of a prism = __________ + _________.
Lateral area + Area of two ends
9) How many faces in pentagonal prism? 7
10) Write the number of vertices in octagonal prism. 16
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19. Refreshment Time
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20. Lets play a Game http://www.miniclip.com/games/santa-balls-2/en/
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21. The formula for base area = lw Plug-in l = 17 and w = 5 lw = (17)(5)
1) Find the base area of the right rectangular prism.
Solution:
The formula for base area = lw
Plug-in l = 17 and w = 5
lw = (17)(5)
= 85
Base area of the prism is 85 ft2
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22. Surface area of cylinder = 2πr (r +h) 2136.56 = 2 * 3.14* 17 ( 17 + h)
2) The surface area of the cylinder is cm2, radius is 17cm. Find the height. (π =3.14)
Solution:
Surface area of cylinder = 2πr (r +h)
= 2 * 3.14* 17 ( 17 + h)
= ( 17+h)
= h
solve for h h = 3.01
So the height of the cylinder = 3 cm
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23. Area of each side is: L = 3 ft * 6 ft = 18 ft2
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.
Solution: The surface area of a prism is the sum of the area of all the sides plus the area of the two bases.
If B is the area of one base and L is the area of one side, Prism's Area = 6*L + 2*B
The area of one hexagonal base is: B = 0.5 * r * base =0.5 * 2.6 ft * 3 ft * 6 = 23.4 ft2
Area of each side is: L = 3 ft * 6 ft = 18 ft2
Prism's Area = 6*L + 2*B = 6*18 ft2 + 2*23.4 ft2
= 108 ft ft2 = ft2
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24. surface area of a cylinder = 2*r2 + 2rh
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*r2 + 2rh
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25. 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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26. Practice gives success
You did great in your lesson today !
Practice gives success
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