Slide 1

Chapter 6: Perimeter, Area, and Volume Regular Math Slide 2 Section 6.1: Perimeter & Area of Rectangles & Parallelograms Perimeter the distance around the OUTSIDE of a figure Area the number of square units INSIDE a figure Slide 3 Finding the Perimeter of Rectangles and Parallelograms Find the perimeter of each figure. P = S + S + S + S P = 26 + 20 + 26 + 20 P = 92 feet Slide 4 Try this one on your own P = S + S + S + S P = 17.5x + 11x + 17.5x + 11x P = 57X units Find the perimeter of each figure. Slide 5 Using a Graph to Find Area Graph each figure with the given vertices. Then find the area of each figure. (-3, -1), (-3, 4), (1, 4), (1, -1) A = bH b = base ; H = height A = 4 X 5 A = 20 units squared Slide 6 Try this one on your own Graph each figure with the given vertices. Then find the area of the figure. (-4, 0), (2, 0), (4, 3), (-2, 3) A = bH A = 6 x 3 A = 18 units squared Slide 7 Finding Area and Perimeter of a Composite Figure Step One: Fill in the missing sides. Step Two: Solve for Perimeter Step Three: Break the figure into rectangles. Step Four: Solve for Area of each rectangle. Step Five: Add the areas of each individual rectangles. Find the perimeter and area of the figure. Slide 8 Section 6.2: Perimeter and Area of Triangles and Trapezoids Find the perimeter of each figure. P = S + S + S P = 22 + 22 + 27 P = 71 feet Slide 9 Try this one on your own Find the perimeter of each figure. P = S + S + S P = 2.5x + 5y + 2x + 2x + 4y P = 6.5x + 9y Slide 10 Find the area of triangles and trapezoids. Graph and find the area of each figure with the given vertices. (-1,-3), (0,2), (3,2), (3, -3) A = x h x (b1 + b2) A = x 5 x (4 +3) A = x 5 x (7) A = 2.5 x 7 A =17.5 units squared Slide 11 Try this one on your own A = x h x (B1 + B2) A = x 3 x (3 + 5) A = x 3 x (8) A = 1.5 x 8 A = 12 units squared Graph and find the area of each figure with the given vertices. (-3,-2), (-3,1), (0,1), (2, -2) Slide 12 Section 6.3: The Pythagorean Theorem Slide 13 Example 1: Finding the length of the hypotenuse. Find the length of the hypotenuse. Slide 14 Graph the triangle with coordinates (6,1), (0,9), and (0,1). Find the length of the hypotenuse. Slide 15 Try this one on your own Find the length of the hypotenuse. C = 6.40 Graph the triangle with the following coordinates (1,-2), (1,7), and (13,-2). A = 9 B = 12 Find the length of the hypotenuse. C = 15 Slide 16 Example 2: Finding the length of a Leg in a Right Triangle Solve for the unknown side in the right triangle. Slide 17 Try this one on your own Solve for the unknown side in the right triangle. b = 24 Slide 18 Example 3: Using the Pythagorean Theorem to Find Area Use the Pythagorean Theorem to find the height of the triangle. Then, use the height to find the area of the triangle. Slide 19 Try this one on your own Use the Pythagorean Theorem to find the height of the triangle. h = square root of 20 or 4.47 Then, use the height to find the area of the triangle. A = 17.89 units squared Slide 20 Section 6.4: Circles Slide 21 Finding the circumference of a Circle. Find the circumference of each circle, both in terms of pi and to the nearest tenth. Use 3.14 for pi. Circle with radius 5 cm Circle with diameter 1.5 in Slide 22 Try these on your own Find the circumference of each circle, both in terms of pi and to the nearest tenth. Use 3.14 for pi. Circle with radius 4 m C = 8pi m or 25.1 m Circle with diameter 3.3 ft C = 3.3pi or 10.4 ft Slide 23 Finding the Area of a Circle. Find the area of each circle, both in terms of pi and to the nearest tenth. Use 3.14 for pi. Circle with radius 5 cm Circle with diameter 1.5 in Slide 24 Try these on your own Find the area of each circle, both in terms of pi and to the nearest tenth. Use 3.14 for pi. Circle with radius 4 in A = 16pi inches squared or 50.2 inches squared Circle with diameter 3.3 m A = 2.7225pi meters squared or 8.5 meters squared Slide 25 Finding Area and Circumference on a Coordinate Plane. Graph the circle with center (-1,1) that passes through (-1,3). Find the area and circumference, both in terms of pi and to the nearest tenth. Use 3.14 for pi. Step One: Graph Circle Step Two: Find the radius Step Three: Use the Area and Circumference Formula Slide 26 Try this one on your own Graph the circle with center (-2,1) that passes through (1,-1). Find the area and circumference, both in terms of pi and to the nearest tenth. Use 3.14 for pi. A = 9pi units squared and 28.3 units squared C = 6pi units and 18.8 units Slide 27 A bicycle odometer recorded 147 revolutions of a wheel with diameter 4/3 ft. How far did the bicycle travel? Use 22/7 for pi. The distance traveled is the circumference of the wheel times the number of revolutions. C = pi(d) = (22/7) (4/3) = 88/21 Circumference x Revolutions 88/21 x 147 = 616 feet Slide 28 Try this one on your own A Ferris wheel has a diameter of 56 feet and makes 15 revolutions per ride. How far would someone travel during a ride? Use 22/7 for pi. C = 22/7(56) = 176 feet Distance = 176 (15) = 2640 feet Slide 29 Section 6.5: Drawing Three Dimensional Figures Example 1: Drawing a Rectangular Box Use isometric dot paper to sketch a rectangular box that is 4 units long, 2 units wide, and 3 units high. Step 1: Lightly draw the edges of the bottom face. It will look like a parallelogram. 2 units by 4 units Step 2: Lightly draw the vertical line segments from the vertices of the base. 3 units high Step 3: Lightly draw the top face by connecting the vertical lines to form a parallelogram. 2 units by 4 units Step 4: Darken the lines. Use solid lines for the edges that are visible and dashed lines for the edges that are hidden. Slide 30 Example 2: Sketching a One-Point Perspective Drawing Step 1: Draw a rectangle. This will be the front face. Label the vertices A through D. Step 2: Mark a vanishing point V somewhere above your rectangle, and draw a dashed line from each vertex to V. Step 3: Choose a point G on line BV. Lightly draw a smaller rectangle that has G as one of its vertices. Step 4: Connect the vertices of the two rectangles along the dashed lines. Step 5: Darken the visible edges, and draw dashed segments for the hidden edges. Erase the vanishing point and all the lines connecting it to the vertices. Slide 31 Example 3: Sketching a Two-Point Perspective Drawing Step 1: Draw a vertical segment and label it AD. Draw a horizontal line above segment AD. Label vanishing points V and W on the line. Draw dashed segments AV, AW, DV, and DW. Step 2: Label point C on segment DV and point E on segment DW. Draw vertical segments through C and E. Draw segment EV and CW. Step 3: Darken the visible edges. Erase horizon lines and dashed segments. Slide 32 Section 6.6: Volume of Prisms and Cylinders Slide 33 Example 1: Finding the Volume of Prisms and Cylinders Find the volume of each figure to the nearest tenth. Step One: Figure out what formula to use. Step Two: Plug the numbers into the formula. Step Three: Solve Slide 34 Try this one on your own Find the volume of each figure to the nearest tenth. Slide 35 Example 2: Exploring the Effects of Changing Dimensions A juice can has a radius of 1.5 inches and a height of 5 inches. Explain whether doubling the height of the can would have the same effect on the volume as doubling the radius. OriginalDouble Radius Double Height Slide 36 Try this one on your own.. A juice can has a radius of 2 inches and a height of 5 inches. Explain whether tripling the height would have the same effect on the volume as tripling the radius. Slide 37 Example 1: Finding the Volume of Prisms and Cylinders Find the volume of each figure to the nearest tenth. A rectangular prism with base 1 meter by 3 meters and height of 6 meters Slide 38 Try these on your own Find the volume of each figure to the nearest tenth. A rectangular prism with base 2 cm by 5 cm and a height of 3cm Slide 39 Example 2: Exploring the Effects of Changing Dimensions A juice box measures 3 inches by 2 inches by 4 inches. Explain whether doubling the length, width, or height of the box would double the amount of juice the box holds. OriginalLengthWidthHeight Slide 40 Try this one on your own A juice box measures 3 inches by 2 inches by 4 inches. Explain whether tripling the length, width, or height would triple the amount of juice the box holds. OriginalLengthWidthHeight Slide 41 Example 3: Construction Application Kansai International Airport is a man-made island that is a rectangular prism measuring 60 ft deep, 4000 ft wide, and 2.5 miles long. What is the volume of rock, gravel, and concrete that was needed to build the island? Try this one on your own A section of an airport runway is a rectangular prism measuring 2 feet thick, 100 feet wide, and 1.5 miles long. What is the volume of material that was needed to build the runway? Slide 42 Example 4: Finding the Volume of Composite Figures Find the volume of the milk carton. Slide 43 Try this one on your own Find the volume of the barn. Slide 44 Section 6.7: Volume of Pyramids and Cones Slide 45 Example 1: Finding the Volume of Pyramids and Cones Find the volume of each figure. Try this one on your own Find the volume of each figure. Slide 46 Example 2: Exploring the Effects of Changing Dimensions A cone has a radius 7 feet and height 14 feet. Explain whether tripling the height would have the same effect on the volume of the cone as tripling the radius. OriginalTriple HeightTriple Radius Slide 47 Try this one on your own A cone has a radius 3 feet and height 4 feet. Explain whether doubling the height would have the same effect on the volume as doubling the radius. OriginalDouble HeightDouble Radius Slide 48 Example 1: Finding the Volume of Pyramids and Cones Find the volume of each figure. Slide 49 Try these on your own Find the volume of each figure. Slide 50 Example 3: Social Studies Application The Great Pyramid of Giza is a square pyramid. Its height is 481 feet, and its base has 756 feet sides. Find the volume of the pyramid. Try these on your own The pyramid of Kukulcan in Mexico is a square pyramid. Its height is 24 meters and its base has 55 meter sides. Find the volume of the pyramid. Slide 51 Section 6.8: Surface Area of Prisms and Cylinders Slide 52 Example 1: Finding Surface Area Find the surface area of each figure. Try this one on your own Slide 53 Find the surface area of each figure. Slide 54 Example 1: Finding Surface Area Finding the surface area of each figure. Try this one on your own Finding the surface area of each figure. Slide 55 Example 2: Exploring the Effects of Changing Dimensions A cylinder has a diameter of 8 inches and a height of 3 inches. Explain whether doubling the height would have the same effect on the surface area as doubling the radius. OriginalDouble HeightDouble Radius Slide 56 Try this one on your own A cylinder has a diameter of 8 inches and a height of 3 inches. Explain whether tripling the height would have the same effect on the surface area as tripling the radius. OriginalTriple RadiusTriple Height Slide 57 Example 3: Art Application A web site advertises that it can turn your photo into an anamorphic image. To reflect the picture, you need to cover a cylinder that is 32mm in diameter and 100 mm tall with reflective material. How much reflective material do you need? Try this one on your own A cylindrical soup can has a radius of 7.6 cm and is 11.2 cm tall. What is the area of the label that covers the side of the can? Slide 58 Section 6.9: Surface Area of Pyramids and Cones Slide 59 Example 1: Finding Surface Area Find the surface area of each figure. Try this one on your own Find the surface area of each figure. Slide 60 Try this one on your own Find the surface area of each figure. Slide 61 Example 1: Finding Surface Area Try this one on your own Find the surface area of each figure. Slide 62 Example 2: Exploring the Effects of Changing Dimensions A cone has a diameter 8 in. and slant height 5 in. Explain whether doubling the slant height would have the same effect on the surface area as doubling the radius. OriginalDouble Slant HeightDouble Radius Slide 63 Try this one on your own A cone has diameter of 8 in. and slant height 3 in. Explain whether tripling the slant height would have the same effect on the surface area as tripling the radius. OriginalTriple RadiusTriple Slant Height Slide 64 Example 3: Life Science Application An ant lion pit is an inverted cone with the dimensions shown. What is the lateral surface area of the pit? Slide 65 Try this one on your own The upper portion of an hourglass is approximately an inverted cone with the given dimensions. What is the lateral surface area of the upper portion of the hourglass? Slide 66 Section 6.10: Spheres Slide 67 Example 1: Finding the Volume of a Sphere Find the volume of a sphere with a radius of 6 ft, both in terms of pi and to the nearest tenth. Try this one on your own Find the volume of a sphere with radius 9 cm, both in terms of pi and to the nearest tenth. Slide 68 Slide 69 Example 2: Finding Surface Area of a Sphere Find the surface area, both in terms of pi and to the nearest tenth. Try this one on your own Find the surface area, both in terms of pi and to the nearest tenth. Slide 70 Example 3: Comparing Volumes and Surface Areas Compare the volume and surface area of a sphere with radius 21 cm with that of a rectangular prism measuring 28 x 33 x 42cm. Sphere Volume Sphere Surface Area Prism Volume Sphere Surface Area Slide 71 Try this one on your own Compare volumes and surface areas of a sphere with radius 42 cm and a rectangular prism measuring 44 cm by 84 cm by 84 cm. Sphere Volume Sphere Surface Area Prism Volume Prism Surface Area