# Surface Area of Prism and Cylinder

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

Warm Up Q1. Draw a top and a front view of each figure. 1. 2.
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Warm Up Make a perspective drawing of each figure by using the top , side and front views as shown. 3. 4. Confidential

Warm Up Make a perspective drawing of each figure by using the top , side and front views as shown. 5. Confidential

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. Confidential

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. Confidential

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. Confidential

Examples of prism Triangle Prism Rectangular Prism Pentagonal Prism
Hexagonal Prism Octagonal Prism Confidential

Figures of prisms Triangular prism Note: A prism is named according to the shape of its base. Confidential

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 Confidential

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 Confidential

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 Confidential

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 Confidential

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 Confidential

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 Confidential

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 Confidential

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 Confidential

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 Confidential

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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 Confidential

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 Confidential

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 Confidential

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 Confidential

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 Confidential

Practice gives success
You did great in your lesson today ! Practice gives success Confidential