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Grade 6 Surface Area of Prism and Cylinder

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2 Warm Up Q1. Draw a top and a front view of each figure. 1. 2.

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3 3. Warm Up Make a perspective drawing of each figure by using the top, side and front views as shown. 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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Let Us Review 5 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 6 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 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. Lets get started

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

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Figures of prisms 9 Triangular prism Note: A prism is named according to the shape of its base.

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Edges and vertices Solid figureNumber of faces Number of edges Number of vertices Triangular prism 596 Rectangular prism 6128 Pentagonal prism 71510 Hexagonal prism 81812 Octagonal prism 102416 10

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Surface Area of Rectangular prisms 11 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 12 Find the surface area of a rectangular prism with 5 cm long, 3 cm wide and 2 cm. high Surface Area of Rectangular prism = 2·L·W + 2·L·H + 2·W·H Solution:- =2.5.3+2.5.2+2.3.2 =30 + 20 + 12 = 62 cm 2

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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 = r 2. There are two ends so their combined surface area is 2* r 2. Surface area of the side = circumference times the height or 2 rh. The entire formula for the surface area of a cylinder is 2* r 2 + 2 rh

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Figures of cylinder 15 h r h is the height of the cylinder, r is the radius of the top Surface area of a cylinder = 2* r 2 + 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* r 2 + 2 rh = 2* 2 2 + 2 (2)(5) = 8 + 20 = 28 cm 2 where = 3.14 = 28 * 3.14 cm 2 = 87.92 cm 2

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17 Lets take a break!!

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18 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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19 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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20 1) Find the base area of the right rectangular prism.

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2) The surface area of the cylinder is 2136.56 cm 2, radius is 17cm. Find the height. (π =3.14) 21

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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. 22

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23 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* r 2 + 2 rh Lets review what we have learned in our lesson

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Types of prism 24 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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25 You did great in your lesson today !

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