Presentation on theme: "Surface Area of 3 – Dimensional Figures"— Presentation transcript:
1 Surface Area of 3 – Dimensional Figures Cubes and Rectangular Prisms
2 DefinitionSurface area is the sum of the areas of all the surfaces of a 3 – Dimensional figure.It is basically the outside layer or surface.Example: When you paint a wall, you are painting the surface of the wall.
3 Surface Area of CubesRemember that a cube is made up of squares on all sides. There are 6 sides to a cube, just like dice. Therefore, there are 6 squares total. To find the surface area, find the area of one square and then multiply by 6. Simply use the following formula.S.A. = 6s2
4 Example Find the surface area of the cube. 4 cm4 cmFind the surface area of the cube.Recall that all of the sides of a square are the same length. So, all you have to do is multiply the sides.Find the area first. The length and the width are both 4 cm. 4 x 4 = 16. Thus, the area of one square is 16 cm2. Now multiply by 6 and we see that the surface area is 96 cm2.
5 YOUR TURN!!! Find the surface area of the following cube. 7 mm7 mmFind the surface area of the following cube.What is the length and width of the cube? 7 mmNow, find the area of one square. 7 x 7 = 49. Thus, the area of one square is 49 mm2.Take this and multiply by 6 and 49 x 6 =294 mm2.So, the surface area of the cube is 294 mm2.
6 Rectangular PrismsTo find the surface area of a prism, you have to find the areas of all the sides and add them up.Understand that there are still 6 sides to a prism and that opposite sides are the same shape.To find the surface area of a rectangular prism use the following formula.S.A. = 2(wh + lh + lw)
7 Example Find the surface area of the prism. S.A. = 2(1 x x x 1)S.A. = 2 ( )S.A. = 2 (103)S.A. = 206The surface area is 206 m2. Surface area is just like finding the regular area. The unit of measurement is squared.
8 TAKE THE CHALLENGE! You find the surface area of the following prism.
9 CHALLENGE Cont. S.A. = 2(4 x 7 + 26 x 7 + 26 x 4) The surface area is 628 ft2
10 SAMPLE ARMT QUESTIONDavid has two shapes he is painting for a project. For each of the two shapes, he will paint only the outside including the lid.One shape is a cylindrical can with a radius of 4 inches and a height of 9 inches.The other shape is a rectangular prism-shaped box. The box is 3 inches wide, 8 inches long, and 5 inches high.Which shape has the greater surface area for David to paint?
11 Sample ARMT Question Cont. First, find the surface area of the cylinder.Formula: (2 x 3.14 x r x h) + (2 x 3.14 x r2)Stick the numbers in directly.(2 x 3.14 x 4 x 9) + (2 x 3.14 x 4 x 4)This equalsAdd these together and the surface area of the cylinder is square inches.
12 Sample ARMT Question Cont. Next, find the surface area of the rectangular prism.Formula: 2(wh + lh + lw)Stick the numbers in directly.2(3·5 + 8·5 + 8·3)This equals 2( )This equals 2(79) = 158The surface area of the rectangular prism is 158 square inches.
13 ANSWER The cylinder has a surface area of 326.56 square inches. The rectangular prism has a surface area of 158 square inches.The cylindrical can has the greater surface area to paint.