10-7 Surface Area Course 1 Warm Up Warm Up Lesson Presentation Lesson Presentation Problem of the Day Problem of the Day
Course Surface Area 6 th Grade Math HOMEWORK Page 532 #1-6
Our Learning Goal Students will be able to find the perimeter and area of polygons; find the area and circumference of circles and find the surface area and volume of 3D shapes.
Our Learning Goal Assignments Learn to find the perimeter and missing side lengths of a polygon. Learn to estimate the area of irregular figures and to find the area of rectangles, triangles, and parallelograms. Learn to break a polygon into simpler parts to find its area. Learn to make a model to explore how area and perimeter are affected by changes in the dimensions of a figure. Learn to identify the parts of a circle and to find the circumference and area of a circle. Learn to name solid figures. Learn to find the surface areas of prisms, pyramids, and cylinders. Learn to estimate and find the volumes of rectangular prisms and triangular prisms. Learn to find volumes of cylinders.
Today’s Learning Goal Assignment Learn to find the surface areas of prisms, pyramids, and cylinders. Course Surface Area
Warm Up Identify the figure described. 1. two parallel congruent faces, with the other faces being parallelograms 2. a polyhedron that has a vertex and a face at opposite ends, with the other faces being triangles prism pyramid Course Surface Area
Problem of the Day Which figure has the longer side and by how much, a square with an area of 81 ft 2 or a square with perimeter of 84 ft? A square with a perimeter of 84 ft; by 12 ft Course Surface Area
Vocabulary surface area net Insert Lesson Title Here Course Surface Area
The surface area of a solid figure is the sum of the areas of its surfaces. To help you see all the surfaces of a solid figure, you can use a net. A net is the pattern made when the surface of a solid figure is layed out flat showing each face of the figure. Course Surface Area
Additional Example 1A: Finding the Surface Area of a Prism Find the surface area S of the prism. A. Method 1: Use a net. Draw a net to help you see each face of the prism. Use the formula A = lw to find the area of each face. Course Surface Area
Additional Example 1A Continued A: A = 5 2 = 10 B: A = 12 5 = 60 C: A = 12 2 = 24 D: A = 12 5 = 60 E: A = 12 2 = 24 F: A = 5 2 = 10 S = = 188 Add the areas of each face. The surface area is 188 in 2. Course Surface Area
Additional Example 1B: Finding the Surface Area of a Prism Find the surface area S of each prism. B. Method 2: Use a three-dimensional drawing. Find the area of the front, top, and side, and multiply each by 2 to include the opposite faces. Course Surface Area
Additional Example 1B Continued Front: 9 7 = 63 Top: 9 5 = 45 Side: 7 5 = 2 = 2 = 2 = 70 S = = 286Add the areas of each face. The surface area is 286 cm 2. Course Surface Area
Try This: Example 1A Find the surface area S of the prism. A. Method 1: Use a net. Draw a net to help you see each face of the prism. Use the formula A = lw to find the area of each face. 3 in. 11 in. 6 in. 11 in. 6 in. 3 in. A B C DE F Course Surface Area
Try This: Example 1A A: A = 6 3 = 18 B: A = 11 6 = 66 C: A = 11 3 = 33 D: A = 11 6 = 66 E: A = 11 3 = 33 F: A = 6 3 = 18 S = = 234 Add the areas of each face. The surface area is 234 in in. 6 in. 3 in. A B C DE F Course Surface Area
Try This: Example 1B Find the surface area S of each prism. B. Method 2: Use a three-dimensional drawing. Find the area of the front, top, and side, and multiply each by 2 to include the opposite faces. 6 cm 10 cm 8 cm top front side Course Surface Area
Try This: Example 1B Continued Front: 10 8 = 80 Top: 10 6 = 60 Side: 8 6 = 2 = 2 = 2 = 96 S = = 376Add the areas of each face. The surface area is 376 cm 2. 6 cm 10 cm 8 cm top front side Course Surface Area
The surface area of a pyramid equals the sum of the area of the base and the areas of the triangular faces. To find the surface area of a pyramid, think of its net. Course Surface Area
Additional Example 2: Finding the Surface Area of a Pyramid Find the surface area S of the pyramid. S = area of square + 4 (area of triangular face) S = 28 S = Substitute. S = s ( bh) 1 2 __ S = ( 7 8) 1 2 __ S = 161 The surface area is 161 ft 2. Course Surface Area
Try This: Example 2 Find the surface area S of the pyramid. S = area of square + 4 (area of triangular face) S = 25 S = Substitute. S = s ( bh) 1 2 __ S = ( 5 10) 1 2 __ S = 125 The surface area is 125 ft 2. 5 ft 10 ft 5 ft Course Surface Area
The surface area of a cylinder equals the sum of the area of its bases and the area of its curved surface. To find the area of the curved surface of a cylinder, multiply its height by the circumference of the base. Helpful Hint Course Surface Area
Additional Example 3: Finding the Surface Area of a Cylinder Find the surface area S of the cylinder. Use 3.14 for , and round to the nearest hundredth. S = area of lateral surface + 2 (area of each base) Substitute. S = h (2r) + 2 (r 2 ) S = 7 (2 4) + 2 ( 4 2 ) ft Course Surface Area
Additional Example 3 Continued Find the surface area S of the cylinder. Use 3.14 for , and round to the nearest hundredth. S 7 8(3.14) + 2 16(3.14) S 7 The surface area is about ft 2. Use 3.14 for . S S S = 7 8 + 2 16 Course Surface Area
Try This: Example 3 Find the surface area S of the cylinder. Use 3.14 for , and round to the nearest hundredth. S = area of lateral surface + 2 (area of each base) Substitute. S = h (2r) + 2 (r 2 ) S = 9 (2 6) + 2 ( 6 2 ) 6 ft 9 ft Course Surface Area
Try This: Example 3 Continued Find the surface area S of the cylinder. Use 3.14 for , and round to the nearest hundredth. S 9 12(3.14) + 2 36(3.14) S 9 The surface area is about ft 2. Use 3.14 for . S S S = 9 12 + 2 36 Course Surface Area
Lesson Quiz Find the surface area of each figure. Use 3.14 for . 1. rectangular prism with base length 6 ft, width 5 ft, and height 7 ft 2. cylinder with radius 3 ft and height 7 ft 3. Find the surface area of the figure shown. Insert Lesson Title Here Course Surface Area 214 ft ft ft 2