Grade 6 Surface Area of Prism and Cylinder

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

3 3. Warm Up Make a perspective drawing of each figure by using the top, side and front views as shown. 4.

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

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.

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.

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

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

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

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

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

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:- = = = 62 cm 2

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

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  rh

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  rh

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  rh = 2*   (2)(5) = 8  + 20  = 28  cm 2 where  = 3.14 = 28 * 3.14 cm 2 = cm 2

17 Lets take a break!!

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 ______.

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.

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

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

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

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  rh Lets review what we have learned in our lesson

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

25 You did great in your lesson today !